lehrkraefte:blc:miniaufgaben:kw19-2024 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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==== 6. Mai 2024 bis 10. Mai 2024 ====
=== Dienstag 7. Mai 2024 ===
Mit Hilfe des TR, berechnen Sie die Nullstellen, Extremalstellenkandidaten und Wendestellenkandidaten. 
Machen Sie eine Tabelle mit diesen $x$-Werten sowie die zugehörigen $y$-Werte und Steigungen. 
Für Extremalstellenkandidaten notieren Sie zusätzlich das Vorzeichen der zweiten Ableitung.
Skizzieren Sie dann mit diesen Informationen den Graphen.
<JS>miniAufgabe("#exokurvendiskussionMitTRquartic","#solkurvendiskussionMitTRquartic",
[["$f(x) = -\\frac{1}{48}\\left(3x^{4}+4x^{3}-36x^{2}+0+94\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -3.88 &nbsp; </td><td> &nbsp; -3.00 &nbsp; </td><td> &nbsp; -1.78 &nbsp; </td><td> &nbsp; -1.65 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.11 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.97 &nbsp; </td><td> &nbsp; .27 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -1.95 &nbsp; </td><td> &nbsp; -1.23 &nbsp; </td><td> &nbsp; -.62 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 5.07 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.05 &nbsp; </td><td> &nbsp; -2.03 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.01 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -7.88 &nbsp; </td><td> &nbsp; -3.75 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; .27 &nbsp; </td><td> &nbsp; 1.50 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -2.50 </td></tr></table>\n\n<br><svg height=\"197.02667\" viewBox=\"0 0 302.69333 197.02667\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 197.02667)\"><path d=\"m65.4844 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m380.418 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m695.348 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1010.28 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1640.14 74.9336v1259.7264\" 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630.602)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 664.1992 630.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 703.1992 630.602)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 978.6012 630.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1017.6012 630.602)\"><tspan x=\"0 61.019676 92.459526\" y=\"0\">112</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1367.9992 61.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1406.9992 61.2)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1367.9992 376.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1406.9992 376.2)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-62.760201\">1</tspan><tspan x=\"-3.9\" y=\"-94.260201\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2020.8002 640.802)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-67.440201\" y=\"-77.880096\">y</tspan></text></g></svg>\n"], ["$f(x) = -\\frac{1}{182}\\left(3x^{4}-8x^{3}-66x^{2}+144x+290\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -4.11 &nbsp; </td><td> &nbsp; -3.00 &nbsp; </td><td> &nbsp; -1.36 &nbsp; </td><td> &nbsp; -1.36 &nbsp; </td><td> &nbsp; 1.00 &nbsp; </td><td> &nbsp; 2.69 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 1.52 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.01 &nbsp; </td><td> &nbsp; -1.99 &nbsp; </td><td> &nbsp; -1.10 &nbsp; </td><td> &nbsp; -.36 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 3.06 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.36 &nbsp; </td><td> &nbsp; -1.36 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .83 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -3.71 &nbsp; </td><td> &nbsp; -1.84 &nbsp; </td><td> &nbsp; -.01 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .79 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -1.38 </td></tr></table>\n\n<br><svg height=\"150.73334\" viewBox=\"0 0 302.69333 150.73334\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 150.73333)\"><path d=\"m46.9609 111.152v889.218\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m269.266 111.152v889.218\" 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font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 276 484.801)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 460.199 484.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 499.199 484.801)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 682.199 484.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 721.199 484.801)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 904.199 484.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 943.199 484.801)\"><tspan x=\"0 42.540222 64.740227 86.940224 109.26012\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1197.601 96.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1236.601 96.602)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1197.601 319.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1236.601 319.2)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-44.280102\">1</tspan><tspan x=\"-3.9\" y=\"-66.540298\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2099.999 492.001)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-92.039803\" y=\"-57.960201\">y</tspan></text></g></svg>\n"], ["$f(x) = -\\frac{1}{586}\\left(3x^{4}+8x^{3}-96x^{2}-384x+803\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -4.00 &nbsp; </td><td> &nbsp; -3.07 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; 1.59 &nbsp; </td><td> &nbsp; 1.73 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 5.60 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; -1.80 &nbsp; </td><td> &nbsp; -1.89 &nbsp; </td><td> &nbsp; -1.99 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .14 &nbsp; </td><td> &nbsp; 1.68 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.14 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .99 &nbsp; </td><td> &nbsp; .99 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.39 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.32 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; .24 &nbsp; </td><td> &nbsp; .04 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.98 &nbsp; </td><td> &nbsp; -2.05 </td></tr></table>\n\n<br><svg height=\"136.16\" viewBox=\"0 0 313.13333 136.16\" width=\"313.13333\" 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3.797 8.48 8.476z\" stroke=\"#000\"/><path d=\"m1107.57 290.668 423.78 417.418\" stroke=\"#000\"/><path d=\"m1808.92 824.625c0 4.68-3.79 8.477-8.47 8.477s-8.48-3.797-8.48-8.477c0-4.684 3.8-8.477 8.48-8.477s8.47 3.793 8.47 8.477z\" stroke=\"#000\"/><path d=\"m1588.56 824.625h423.77\" stroke=\"#000\"/><path d=\"m2147.94 468.652c0 4.68-3.79 8.477-8.48 8.477-4.67 0-8.47-3.797-8.47-8.477 0-4.679 3.8-8.476 8.47-8.476 4.69 0 8.48 3.797 8.48 8.476z\" stroke=\"#000\"/><path d=\"m2226.34 256.766-175.87 423.773\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 74.3984 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 113.3984 399)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 285.6014 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 324.6014 399)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 497.9994 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 536.9994 399)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 710.3974 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 749.3974 399)\"><tspan x=\"0 40.380074 61.499973 82.740227 103.98007 125.09998 146.34023\" y=\"0\">1123456</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 991.7994 31.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1030.7994 31.199)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 991.7994 243)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1030.7994 243)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-42.239799\">1</tspan><tspan x=\"-3.9\" y=\"-63.3601\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2275.7994 405.601)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-130.08\" y=\"-55.799999\">y</tspan></text></g></svg>\n"], ["$f(x) = \\frac{1}{607}\\left(3x^{4}-8x^{3}-96x^{2}+384x+578\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -5.75 &nbsp; </td><td> &nbsp; -4.00 &nbsp; </td><td> &nbsp; -1.73 &nbsp; </td><td> &nbsp; -1.19 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; 3.07 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -.50 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 1.55 &nbsp; </td><td> &nbsp; 1.46 &nbsp; </td><td> &nbsp; 1.37 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; -2.61 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .95 &nbsp; </td><td> &nbsp; .92 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.13 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; 2.10 &nbsp; </td><td> &nbsp; .94 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -.13 &nbsp; </td><td> &nbsp; -.23 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .31 </td></tr></table>\n\n<br><svg height=\"130.67999\" viewBox=\"0 0 302.69333 130.67999\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 130.68)\"><path d=\"m42.9922 42.3906v809.8204\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m245.445 42.3906v809.8204\" 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stroke=\"#000\"/><path d=\"m1676.8 771.23 404.91-56.687\" stroke=\"#000\"/><path d=\"m2075.64 724.664c0 4.473-3.62 8.102-8.1 8.102-4.47 0-8.09-3.629-8.09-8.102s3.62-8.098 8.09-8.098c4.48 0 8.1 3.625 8.1 8.098z\" stroke=\"#000\"/><path d=\"m1865.09 724.664h404.91\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 11.3984 378)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 50.3984 378)\"><tspan x=\"0\" y=\"0\">6</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 214.1994 378)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 253.1994 378)\"><tspan x=\"0\" y=\"0\">5</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 415.8014 378)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 454.8014 378)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 618.6024 378)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 657.6024 378)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 821.3994 378)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 860.3994 378)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1023.0014 378)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1062.0014 378)\"><tspan x=\"0 38.580074 58.860172 79.019928 99.300026\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1296.0014 28.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1335.0014 28.801)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1296.0014 231.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1335.0014 231.602)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-40.2598\">1</tspan><tspan x=\"-3.9\" y=\"-60.479698\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2116.8024 383.399)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-83.760201\" y=\"-53.8801\">y</tspan></text></g></svg>\n"], ["$f(x) = -\\frac{1}{48}\\left(3x^{4}-20x^{3}+12x^{2}+96x-33\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -1.88 &nbsp; </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; .21 &nbsp; </td><td> &nbsp; .33 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; 3.11 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 1.95 &nbsp; </td><td> &nbsp; .25 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -1.97 &nbsp; </td><td> &nbsp; -1.25 &nbsp; </td><td> &nbsp; -.64 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 5.04 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.05 &nbsp; </td><td> &nbsp; -2.03 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.01 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -7.86 &nbsp; </td><td> &nbsp; -3.75 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; .25 &nbsp; </td><td> &nbsp; 1.50 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.50 </td></tr></table>\n\n<br><svg height=\"197.86667\" viewBox=\"0 0 302.69333 197.86667\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g 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18.9-.2851 18.89 1.4023 18.9 3.0508 18.9 4.6562 18.89 6.2106 18.89 7.704 18.9 9.136 18.9 10.5 18.89 11.785 18.9 12.989 18.89 14.101 18.9 15.129 18.9 16.047 18.89 16.859 18.9 17.567 18.9 18.148 18.89 18.61 18.89 18.933 18.9 19.129 18.9 19.172 18.89 19.074 18.9 18.813 18.89 18.398 18.9 17.809 18.9 17.051 18.89 16.109 18.9 14.984 18.9 13.668 18.89 12.149 18.89 10.429 18.9 8.496 18.9 6.348 18.89 3.977 18.9 1.379\" stroke=\"#000\" stroke-dasharray=\"39.7967 39.7967\"/><path d=\"m115.875 710.492c0 6.961-5.641 12.598-12.598 12.598-6.9567 0-12.5973-5.637-12.5973-12.598 0-6.957 5.6406-12.594 12.5973-12.594 6.957 0 12.598 5.637 12.598 12.594z\" stroke=\"#000\"/><path d=\"m40.293 395.563 125.969 626.707\" stroke=\"#000\"/><path d=\"m393.012 1324.61c0 6.96-5.637 12.6-12.594 12.6s-12.598-5.64-12.598-12.6 5.641-12.6 12.598-12.6 12.594 5.64 12.594 12.6z\" stroke=\"#000\"/><path d=\"m65.4844 1324.61h629.8636\" stroke=\"#000\"/><path d=\"m774.078 789.227c0 6.957-5.637 12.597-12.598 12.597-6.957 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stroke=\"#000\"/><path d=\"m1640.14 508.938h629.86\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 34.1992 636.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 73.1992 636.602)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 348.6012 636.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 387.6012 636.602)\"><tspan x=\"0 61.020172 92.460022 124.02017 155.46002\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 737.9992 67.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 776.9992 67.2)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 737.9992 382.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 776.9992 382.2)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-62.819901\">1</tspan><tspan x=\"-3.9\" y=\"-94.260101\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2020.7992 647.399)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-130.44\" y=\"-77.880096\">y</tspan></text></g></svg>\n"], ["$f(x) = -\\frac{1}{50}\\left(3x^{4}-20x^{3}+12x^{2}+96x-28\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -1.86 &nbsp; </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; .21 &nbsp; </td><td> &nbsp; .28 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; 3.11 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 1.78 &nbsp; </td><td> &nbsp; .14 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -1.30 &nbsp; </td><td> &nbsp; -.72 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 4.68 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.97 &nbsp; </td><td> &nbsp; -1.96 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .97 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -7.44 &nbsp; </td><td> &nbsp; -3.60 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; .14 &nbsp; </td><td> &nbsp; 1.44 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.40 </td></tr></table>\n\n<br><svg height=\"198.70667\" viewBox=\"0 0 302.69333 198.70667\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 198.70667)\"><path d=\"m65.4844 87.5313v1259.7187\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m380.418 87.5313v1259.7187\" 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d=\"m796.125 717.395c0 6.957-5.641 12.593-12.598 12.593s-12.597-5.636-12.597-12.593c0-6.961 5.64-12.598 12.597-12.598s12.598 5.637 12.598 12.598z\" stroke=\"#000\"/><path d=\"m944.141 402.461-318.078 626.719\" stroke=\"#000\"/><path d=\"m1337.8 87.5313c0 6.957-5.64 12.5977-12.59 12.5977-6.96 0-12.6-5.6407-12.6-12.5977 0-6.9571 5.64-12.5977 12.6-12.5977 6.95 0 12.59 5.6406 12.59 12.5977z\" stroke=\"#000\"/><path d=\"m1010.28 87.5313h629.86\" stroke=\"#000\"/><path d=\"m1687.38 307.984c0 6.957-5.64 12.598-12.6 12.598s-12.6-5.641-12.6-12.598 5.64-12.597 12.6-12.597 12.6 5.64 12.6 12.597z\" stroke=\"#000\"/><path d=\"m1359.85 2.5 629.86 614.113\" stroke=\"#000\"/><path d=\"m1967.67 490.645c0 6.957-5.64 12.593-12.6 12.593s-12.6-5.636-12.6-12.593c0-6.961 5.64-12.598 12.6-12.598s12.6 5.637 12.6 12.598z\" stroke=\"#000\"/><path d=\"m1640.14 490.645h629.86\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 34.1992 642.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 73.1992 642.602)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 348.6012 642.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 387.6012 642.602)\"><tspan x=\"0 61.020172 92.460022 124.02017 155.46002\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 737.9992 73.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 776.9992 73.801)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 737.9992 388.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 776.9992 388.199)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-62.760201\">1</tspan><tspan x=\"-3.9\" y=\"-94.32\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2020.7992 652.801)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-130.44\" y=\"-77.880096\">y</tspan></text></g></svg>\n"], ["$f(x) = \\frac{1}{142}\\left(3x^{4}-8x^{3}-48x^{2}+0+227\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -1.09 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 2.09 &nbsp; </td><td> &nbsp; 2.43 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 5.20 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 1.03 &nbsp; </td><td> &nbsp; 1.29 &nbsp; </td><td> &nbsp; 1.59 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.46 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .42 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.38 &nbsp; </td><td> &nbsp; -1.42 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 3.81 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; 1.01 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.67 &nbsp; </td><td> &nbsp; -.26 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 2.02 &nbsp; </td><td> &nbsp; 4.43 </td></tr></table>\n\n<br><svg height=\"233.18668\" viewBox=\"0 0 312.74667 233.18668\" width=\"312.74667\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><clipPath id=\"a\"><path d=\"m0 0h2346v1749h-2346z\"/></clipPath><clipPath id=\"b\"><path d=\"m.800781-76.2773h2475.589219v1824.1273h-2475.589219z\"/></clipPath><g clip-path=\"url(#a)\" transform=\"matrix(.13333333 0 0 -.13333333 0 233.18667)\"><g clip-path=\"url(#b)\"><path d=\"m131.094 54.0195v1302.9405\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m391.684 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style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m131.094 54.0195h2084.706\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m131.094 314.605h2084.706\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m131.094 575.195h2084.706\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m131.094 1096.38h2084.706\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m131.094 1356.96h2084.706\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m131.094 846.207v-20.848\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m92.7969 752.758h76.5941v49.203h-76.5941z\" fill=\"#fff\"/><path d=\"m92.7969 752.758h76.5941v49.203h-76.5941z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m391.684 846.207v-20.848\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m353.387 752.758h76.593v49.203h-76.593z\" fill=\"#fff\"/><path d=\"m353.387 752.758h76.593v49.203h-76.593z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m652.273 846.207v-20.848\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m912.863 846.207v-20.848\" 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style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2267.93 835.785-74.98 20.09v-40.18z\"/><path d=\"m2267.93 835.785-74.98 20.09v-40.18z\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m652.273 1334.1v-1332.20156\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m652.273 1409.08-20.093-74.98h40.183z\"/><g fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-miterlimit=\"10\" stroke-width=\"5\"><path d=\"m652.273 1409.08-20.093-74.98h40.183z\" stroke=\"#000\"/><path d=\"m131.094 1105.55 20.847.81 20.848 2.34 20.848 3.67 20.847 4.84 20.844 5.86 20.848 6.72 20.847 7.42 20.848 7.99 20.848 8.41 20.847 8.69 20.848 8.85 20.848 8.89 20.843 8.8 20.848 8.61 20.848 8.31 20.847 7.9 20.848 7.39 20.848 6.81 20.847 6.12 20.844 5.37 20.848 4.53 20.847 3.63 20.848 2.66 20.848 1.63 20.847.56 20.848-.57 20.844-1.74 20.848-2.95 20.847-4.18 20.848-5.45 20.847-6.74 20.848-8.03 20.848-9.34 20.844-10.66 20.847-11.98 20.848-13.28 20.848-14.57 20.847-15.86 20.848-17.11 20.847-18.34 20.848-19.53 20.842-20.69 20.85-21.8 20.85-22.86 20.84-23.88 20.85-24.812 20.85-25.699 20.85-26.508 20.84-27.238 20.85-27.891 20.85-28.453 20.84-28.926 20.85-29.296 20.85-29.567 20.85-29.722 20.84-29.77 20.85-29.695 20.85-29.493 20.84-29.16 20.85-28.695 20.85-28.082 20.85-27.328 20.84-26.422 20.85-25.352 20.85-24.121 20.84-22.726 20.85-21.153 20.85-19.398 20.85-17.461 20.84-15.336 20.85-13.012 20.85-10.488 20.84-7.758 20.85-4.812 20.85-1.656 20.85 1.73 20.84 5.34 20.85 9.187 20.85 13.266 20.84 17.598 20.85 22.175 20.85 27.008 20.85 32.106 20.84 37.461 20.85 43.093 20.85 49.004 20.84 55.196 20.85 61.671 20.85 68.446 20.85 75.515 20.84 82.887 20.85 90.577 20.85 98.57 20.84 106.89 20.85 115.53 20.85 124.52 20.85 133.82 20.84 143.47 20.85 153.48 20.84 163.83\" stroke=\"#000\" stroke-dasharray=\"39.8715 39.8715\"/><path d=\"m141.52 1104.19c0 5.76-4.668 10.42-10.426 10.42s-10.422-4.66-10.422-10.42 4.664-10.42 10.422-10.42 10.426 4.66 10.426 10.42z\" stroke=\"#000\"/><path d=\"m-129.496 1104.19h521.18\" stroke=\"#000\"/><path d=\"m378.652 1171.95c0 5.75-4.664 10.42-10.422 10.42-5.757 0-10.421-4.67-10.421-10.42 0-5.76 4.664-10.43 10.421-10.43 5.758 0 10.422 4.67 10.422 10.43z\" stroke=\"#000\"/><path d=\"m107.641 1062.5 521.179 221.5\" stroke=\"#000\"/><path d=\"m662.695 1250.12c0 5.76-4.668 10.42-10.422 10.42-5.757 0-10.425-4.66-10.425-10.42s4.668-10.42 10.425-10.42c5.754 0 10.422 4.66 10.422 10.42z\" stroke=\"#000\"/><path d=\"m391.684 1250.12h521.179\" stroke=\"#000\"/><path d=\"m1207.33 835.785c0 5.758-4.67 10.422-10.43 10.422-5.75 0-10.42-4.664-10.42-10.422s4.67-10.426 10.42-10.426c5.76 0 10.43 4.668 10.43 10.426z\" stroke=\"#000\"/><path d=\"m1387.13 577.801-377.85 518.579\" stroke=\"#000\"/><path d=\"m1295.93 715.914c0 5.758-4.67 10.422-10.43 10.422-5.75 0-10.42-4.664-10.42-10.422s4.67-10.426 10.42-10.426c5.76 0 10.43 4.668 10.43 10.426z\" stroke=\"#000\"/><path d=\"m1467.91 455.324-364.82 518.574\" stroke=\"#000\"/><path d=\"m1705.05 314.605c0 5.758-4.66 10.426-10.42 10.426s-10.43-4.668-10.43-10.426c0-5.753 4.67-10.421 10.43-10.421s10.42 4.668 10.42 10.421z\" stroke=\"#000\"/><path d=\"m1434.04 314.605h521.18\" stroke=\"#000\"/><path d=\"m2017.76 835.785c0 5.758-4.67 10.422-10.42 10.422-5.76 0-10.43-4.664-10.43-10.422s4.67-10.426 10.43-10.426c5.75 0 10.42 4.668 10.42 10.426z\" stroke=\"#000\"/><path d=\"m1939.58 575.195 135.51 518.575\" stroke=\"#000\"/></g></g></g><g font-size=\"4.98132\"><text font-family=\"CMSY10\" transform=\"matrix(1.3333333 0 0 1.3333333 13.14687967133 131.34653921267)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" transform=\"matrix(1.3333333 0 0 1.3333333 18.34687954133 131.34653921267)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" transform=\"matrix(1.3333333 0 0 1.3333333 47.86661213667 131.34653921267)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" transform=\"matrix(1.3333333 0 0 1.3333333 53.06661200667 131.34653921267)\"><tspan x=\"0 50.219925 76.26017 102.30003 128.33987 154.50003 180.53987\" y=\"0\">1123456</tspan></text><text font-family=\"CMSY10\" transform=\"matrix(1.3333333 0 0 1.3333333 92.26661102667 227.82680346733)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" transform=\"matrix(1.3333333 0 0 1.3333333 97.46661089667 227.82680346733)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" transform=\"matrix(1.3333333 0 0 1.3333333 92.26661102667 193.02680433733)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" transform=\"matrix(1.3333333 0 0 1.3333333 97.46661089667 193.02680433733)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" transform=\"matrix(1.3333333 0 0 1.3333333 92.26661102667 158.30653853867)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" transform=\"matrix(1.3333333 0 0 1.3333333 97.46661089667 158.30653853867)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-51.959801\">1</tspan><tspan x=\"-3.9\" y=\"-78\">2</tspan></text></g><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(1.3333333 0 0 1.3333333 303.14660575467 130.22680590733)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-160.08\" y=\"-66.240196\">y</tspan></text></svg>\n"], ["$f(x) = \\frac{1}{47}\\left(3x^{4}-8x^{3}-30x^{2}+72x+58\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -2.88 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -.78 &nbsp; </td><td> &nbsp; -.66 &nbsp; </td><td> &nbsp; 1.00 &nbsp; </td><td> &nbsp; 2.11 &nbsp; </td><td> &nbsp; 3.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -.25 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 2.02 &nbsp; </td><td> &nbsp; 1.28 &nbsp; </td><td> &nbsp; .65 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; -5.14 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 2.09 &nbsp; </td><td> &nbsp; 2.07 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.03 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; 8.03 &nbsp; </td><td> &nbsp; 3.82 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.26 &nbsp; </td><td> &nbsp; -1.53 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 2.55 </td></tr></table>\n\n<br><svg height=\"237.77333\" viewBox=\"0 0 302.69333 237.77333\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 237.77333)\"><path d=\"m65.4844 66.0859v1574.6541\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m380.418 66.0859v1574.6541\" 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style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m997.68 66.0859h25.2\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1046.28 41.4805h76.61v49.2109h-76.61z\" fill=\"#fff\"/><path d=\"m1046.28 41.4805h76.61v49.2109h-76.61z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m997.68 381.016h25.2\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1046.28 356.41h76.61v49.211h-76.61z\" fill=\"#fff\"/><path d=\"m1046.28 356.41h76.61v49.211h-76.61z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m997.68 695.945h25.2\" 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style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1046.28 1618.21h37.86v45.06h-37.86z\" fill=\"#fff\"/><path d=\"m1046.28 1618.21h37.86v45.06h-37.86z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2007.33 618.965h82.86v68.812h-82.86z\" fill=\"#fff\"/><path d=\"m2007.33 618.965h82.86v68.812h-82.86z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1018.45 1693h78.34v88.18h-78.34z\" fill=\"#fff\"/><path d=\"m1018.45 1693h78.34v88.18h-78.34z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1943.06 695.945h-1940.56\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2018.05 695.945-74.99 20.098v-40.191z\"/><path d=\"m2018.05 695.945-74.99 20.098v-40.191z\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1010.28 1628.73v-1625.62844\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1010.28 1703.73-20.096-75h40.186z\"/><g fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-miterlimit=\"10\" stroke-width=\"5\"><path d=\"m1010.28 1703.73-20.096-75h40.186z\" stroke=\"#000\"/><path d=\"m65.4844 903.668 18.8984-110.93 18.8942-101.468 18.895-92.375 18.898-83.649 18.895-75.289 18.894-67.277 18.899-59.614 18.894-52.293 18.895-45.308 18.898-38.652 18.895-32.317 18.894-26.301 18.899-20.5895 18.894-15.1914 18.895-10.0821 18.898-5.2656 18.895-.7422 18.894 3.5117 18.899 7.4883 18.894 11.1992 18.895 14.6526 18.898 17.847 18.895 20.797 18.894 23.508 18.899 25.977 18.894 28.222 18.895 30.243 18.898 32.046 18.895 33.645 18.894 35.031 18.899 36.227 18.894 37.23 18.895 38.043 18.898 38.684 18.895 39.148 18.894 39.446 18.899 39.585 18.894 39.571 18.895 39.406 18.898 39.102 18.895 38.664 18.894 38.093 18.899 37.403 18.894 36.597 18.895 35.68 18.898 34.656 18.895 33.539 18.894 32.324 18.899 31.04 18.897 29.66 18.89 28.21 18.9 26.7 18.89 25.12 18.9 23.5 18.9 21.82 18.89 20.11 18.9 18.36 18.9 16.57 18.89 14.78 18.89 12.95 18.9 11.13 18.9 9.29 18.89 7.46 18.9 5.65 18.89 3.83 18.9 2.05 18.9.29 18.89-1.43 18.9-3.12 18.9-4.75 18.89-6.34 18.89-7.87 18.9-9.33 18.9-10.73 18.89-12.03 18.9-13.26 18.89-14.41 18.9-15.45 18.9-16.39 18.89-17.22 18.9-17.94 18.9-18.53 18.89-19 18.89-19.34 18.9-19.54 18.9-19.58 18.89-19.47 18.9-19.22 18.89-18.79 18.9-18.19 18.9-17.414 18.89-16.453 18.9-15.3 18.9-13.958 18.89-12.406 18.89-10.652 18.9-8.676 18.9-6.484 18.89-4.063 18.9-1.406\" stroke=\"#000\" stroke-dasharray=\"40.3201 40.3201\"/><path d=\"m115.875 695.945c0 6.961-5.641 12.598-12.598 12.598-6.9567 0-12.5973-5.637-12.5973-12.598 0-6.957 5.6406-12.593 12.5973-12.593 6.957 0 12.598 5.636 12.598 12.593z\" stroke=\"#000\"/><path d=\"m166.262 381.016-122.8206 626.714\" stroke=\"#000\"/><path d=\"m393.012 66.0859c0 6.9571-5.637 12.5977-12.594 12.5977s-12.598-5.6406-12.598-12.5977c0-6.957 5.641-12.5976 12.598-12.5976s12.594 5.6406 12.594 12.5976z\" stroke=\"#000\"/><path d=\"m65.4844 66.0859h629.8636\" stroke=\"#000\"/><path d=\"m777.23 617.215c0 6.957-5.64 12.598-12.597 12.598s-12.598-5.641-12.598-12.598 5.641-12.598 12.598-12.598 12.597 5.641 12.597 12.598z\" stroke=\"#000\"/><path d=\"m613.465 302.285 302.332 626.711\" stroke=\"#000\"/><path d=\"m815.02 695.945c0 6.961-5.641 12.598-12.598 12.598s-12.598-5.637-12.598-12.598c0-6.957 5.641-12.593 12.598-12.593s12.598 5.636 12.598 12.593z\" stroke=\"#000\"/><path d=\"m651.258 384.164 302.332 626.716\" stroke=\"#000\"/><path d=\"m1337.8 1332.11c0 6.95-5.64 12.59-12.59 12.59-6.96 0-12.6-5.64-12.6-12.59 0-6.96 5.64-12.6 12.6-12.6 6.95 0 12.59 5.64 12.59 12.6z\" stroke=\"#000\"/><path d=\"m1010.28 1332.11h629.86\" stroke=\"#000\"/><path d=\"m1687.38 1099.06c0 6.96-5.64 12.6-12.6 12.6s-12.6-5.64-12.6-12.6 5.64-12.6 12.6-12.6 12.6 5.64 12.6 12.6z\" stroke=\"#000\"/><path d=\"m1980.26 784.129-607.81 629.861\" stroke=\"#000\"/><path d=\"m1967.67 900.652c0 6.957-5.64 12.598-12.6 12.598s-12.6-5.641-12.6-12.598 5.64-12.597 12.6-12.597 12.6 5.64 12.6 12.597z\" stroke=\"#000\"/><path d=\"m1640.14 900.652h629.86\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 34.1992 621)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 73.1992 621)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 348.6012 621)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 387.6012 621)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 664.1992 621)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 703.1992 621)\"><tspan x=\"0 60.900124 92.460274 123.90012\" y=\"0\">1123</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1052.3982 51.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1091.3982 51.602)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1052.3982 367.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1091.3982 367.2)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-62.760201\">1</tspan><tspan x=\"-3.9\" y=\"-94.260201\">2</tspan><tspan x=\"-3.9\" y=\"-125.7602\">3</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2020.8002 631.802)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-98.880096\" y=\"-109.32\">y</tspan></text></g></svg>\n"], ["$f(x) = \\frac{1}{347}\\left(3x^{4}+4x^{3}-96x^{2}-192x+599\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -4.00 &nbsp; </td><td> &nbsp; -2.66 &nbsp; </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; 1.79 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 5.45 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; .98 &nbsp; </td><td> &nbsp; 1.45 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.25 &nbsp; </td><td> &nbsp; -1.96 &nbsp; </td><td> &nbsp; -.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .51 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.23 &nbsp; </td><td> &nbsp; -1.24 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 3.06 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; .82 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.51 &nbsp; </td><td> &nbsp; -.09 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.38 &nbsp; </td><td> &nbsp; 2.91 </td></tr></table>\n\n<br><svg height=\"136.16\" viewBox=\"0 0 313.13333 136.16\" width=\"313.13333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 136.16)\"><path d=\"m105.344 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m317.23 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m529.121 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m741.008 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1164.78 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1376.67 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1588.56 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1800.45 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2012.33 44.8789v847.5511\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2224.22 44.8789v847.5511\" 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1.4961 21.19 4.6211 21.19 7.9453 21.19 11.4649 21.19 15.1914 21.19 19.1328 21.19 23.289 21.19 27.66 21.18 32.254 21.19 37.078 21.19 42.137 21.19 47.43 21.19 52.961 21.19 58.746 21.19 64.769 21.18 71.059 21.2 77.597 21.18 84.403 21.19 91.476 21.19 98.821\" stroke=\"#000\" stroke-dasharray=\"40.0857 40.0857\"/><path d=\"m113.82 676.301c0 4.683-3.797 8.476-8.476 8.476-4.68 0-8.4768-3.793-8.4768-8.476 0-4.68 3.7968-8.473 8.4768-8.473 4.679 0 8.476 3.793 8.476 8.473z\" stroke=\"#000\"/><path d=\"m-106.543 676.301h423.773\" stroke=\"#000\"/><path d=\"m397.75 775.891c0 4.679-3.797 8.476-8.477 8.476-4.679 0-8.476-3.797-8.476-8.476 0-4.68 3.797-8.477 8.476-8.477 4.68 0 8.477 3.797 8.477 8.477z\" stroke=\"#000\"/><path d=\"m177.387 667.828 423.773 216.125\" stroke=\"#000\"/><path d=\"m749.484 892.43c0 4.679-3.796 8.472-8.476 8.472-4.684 0-8.477-3.793-8.477-8.472 0-4.684 3.793-8.477 8.477-8.477 4.68 0 8.476 3.793 8.476 8.477z\" stroke=\"#000\"/><path d=\"m529.121 892.43h423.774\" stroke=\"#000\"/><path d=\"m1340.65 468.652c0 4.68-3.79 8.477-8.47 8.477-4.69 0-8.48-3.797-8.48-8.477 0-4.679 3.79-8.476 8.48-8.476 4.68 0 8.47 3.797 8.47 8.476z\" stroke=\"#000\"/><path d=\"m1503.8 258.883-343.26 421.656\" stroke=\"#000\"/><path d=\"m1385.14 415.68c0 4.683-3.79 8.476-8.47 8.476s-8.47-3.793-8.47-8.476c0-4.68 3.79-8.473 8.47-8.473s8.47 3.793 8.47 8.473z\" stroke=\"#000\"/><path d=\"m1546.18 203.793-341.14 421.656\" stroke=\"#000\"/><path d=\"m1808.92 53.3516c0 4.6836-3.79 8.4765-8.47 8.4765s-8.48-3.7929-8.48-8.4765c0-4.6797 3.8-8.4727 8.48-8.4727s8.47 3.793 8.47 8.4727z\" stroke=\"#000\"/><path d=\"m1588.56 53.3516h423.77\" stroke=\"#000\"/><path d=\"m2116.16 468.652c0 4.68-3.8 8.477-8.48 8.477s-8.47-3.797-8.47-8.477c0-4.679 3.79-8.476 8.47-8.476s8.48 3.797 8.48 8.476z\" stroke=\"#000\"/><path d=\"m2037.76 256.766 139.85 421.656\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 74.3984 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 113.3984 399)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 285.6014 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 324.6014 399)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 497.9994 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 536.9994 399)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 710.3974 399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 749.3974 399)\"><tspan x=\"0 40.380074 61.499973 82.740227 103.98007 125.09998 146.34023\" y=\"0\">1123456</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 991.7994 31.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1030.7994 31.199)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 991.7994 243)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1030.7994 243)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-42.239799\">1</tspan><tspan x=\"-3.9\" y=\"-63.3601\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2275.7994 405.601)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-130.08\" y=\"-55.799999\">y</tspan></text></g></svg>\n"], ["$f(x) = \\frac{1}{307}\\left(3x^{4}+0-78x^{2}-144x+442\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -3.00 &nbsp; </td><td> &nbsp; -2.08 &nbsp; </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; 1.69 &nbsp; </td><td> &nbsp; 2.08 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 5.46 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 1.35 &nbsp; </td><td> &nbsp; 1.49 &nbsp; </td><td> &nbsp; 1.66 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -.45 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .23 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.13 &nbsp; </td><td> &nbsp; -1.17 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 3.12 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; .54 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.39 &nbsp; </td><td> &nbsp; -.17 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.36 &nbsp; </td><td> &nbsp; 2.99 </td></tr></table>\n\n<br><svg height=\"148.8\" viewBox=\"0 0 312.95999 148.8\" 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font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 85.1992 445.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 124.1992 445.398)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 319.1992 445.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 358.1992 445.398)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 553.1992 445.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 592.1992 445.398)\"><tspan x=\"0 44.819923 68.100021 91.500023 114.90002 138.30002 161.70003\" y=\"0\">1123456</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 858.6012 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" <hr> ");
</JS>
<HTML>
<div id="exokurvendiskussionMitTRquartic"></div>

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<hidden Lösungen>

<HTML>
<div id="solkurvendiskussionMitTRquartic"></div>
<div style='font-size:12px;color:gray;'>ruby extremalstellen-von-polynom-3ten-grades.rb 3</div>
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=== Mittwoch 8. Mai 2024 ===
Mit Hilfe des TR, berechnen Sie die Nullstellen, Extremalstellenkandidaten und Wendestellenkandidaten. 
Machen Sie eine Tabelle mit diesen $x$-Werten sowie die zugehörigen $y$-Werte und Steigungen. 
Für Extremalstellenkandidaten notieren Sie zusätzlich das Vorzeichen der zweiten Ableitung.
Skizzieren Sie dann mit diesen Informationen den Graphen.
<JS>miniAufgabe("#exokurvendiskussionMitTRquadrQuot","#solkurvendiskussionMitTRquadrQuot",
[["$\\displaystyle f(x) = \\frac{\\left(2x+1\\right)\\left(x-3\\right)}{\\left(2x+1\\right)^{2}+1}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -1.46 &nbsp; </td><td> &nbsp; -1.07 &nbsp; </td><td> &nbsp; -.52 &nbsp; </td><td> &nbsp; -.50 &nbsp; </td><td> &nbsp; -.06 &nbsp; </td><td> &nbsp; .27 &nbsp; </td><td> &nbsp; 3.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 1.82 &nbsp; </td><td> &nbsp; 2.01 &nbsp; </td><td> &nbsp; .16 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.51 &nbsp; </td><td> &nbsp; -1.23 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; .68 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -7.04 &nbsp; </td><td> &nbsp; -7.00 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 1.11 &nbsp; </td><td> &nbsp; .14 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -5.21 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 9.21 &nbsp; 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17.551-56.887 17.55-39.23 17.551-23.903 17.551-11.347 17.551-1.539 17.551 5.82 17.546 11.117 17.551 14.774 17.551 17.168 17.551 18.601 17.551 19.34 17.55 19.566 17.551 19.442 17.552 19.07 17.55 18.531 17.55 17.891 17.55 17.195 17.55 16.465 17.55 15.727 17.55 15 17.55 14.289 17.55 13.601 17.55 12.942 17.55 12.312 17.55 11.719 17.55 11.152 17.55 10.621 17.55 10.118 17.55 9.64 17.55 9.196 17.55 8.773 17.55 8.379 17.55 8.004 17.55 7.656 17.55 7.32 17.55 7.016 17.56 6.715 17.55 6.441 17.55 6.18 17.55 5.933 17.54 5.7 17.56 5.48 17.55 5.27 17.55 5.07 17.55 4.887 17.55 4.707 17.55 4.539 17.55 4.375 17.55 4.226 17.55 4.082 17.55 3.946 17.55 3.812 17.55 3.688 17.55 3.57 17.55 3.453 17.55 3.348 17.55 3.246 17.55 3.144 17.55 3.051 17.55 2.957 17.55 2.875 17.55 2.789 17.55 2.711 17.55 2.637 17.56 2.559 17.54 2.492\" stroke=\"#000\" stroke-dasharray=\"40.3233 40.3233\"/><path d=\"m367.547 1423.68c0 7.75-6.285 14.03-14.039 14.03-7.758 0-14.043-6.28-14.043-14.03 0-7.76 6.285-14.04 14.043-14.04 7.754 0 14.039 6.28 14.039 14.04z\" stroke=\"#000\"/><path d=\"m2.5 1181.48 702.012 480.88\" stroke=\"#000\"/><path d=\"m504.438 1490.37c0 7.75-6.286 14.04-14.04 14.04-7.753 0-14.039-6.29-14.039-14.04 0-7.76 6.286-14.05 14.039-14.05 7.754 0 14.04 6.29 14.04 14.05z\" stroke=\"#000\"/><path d=\"m139.391 1490.37h702.015\" stroke=\"#000\"/><path d=\"m697.492 841.004c0 7.754-6.285 14.043-14.039 14.043s-14.043-6.289-14.043-14.043 6.289-14.039 14.043-14.039 14.039 6.285 14.039 14.039z\" stroke=\"#000\"/><path d=\"m732.594 493.508-98.281 698.502\" stroke=\"#000\"/><path d=\"m704.512 784.844c0 7.754-6.285 14.039-14.039 14.039s-14.039-6.285-14.039-14.039 6.285-14.039 14.039-14.039 14.039 6.285 14.039 14.039z\" stroke=\"#000\"/><path d=\"m743.121 433.836-101.789 702.014\" stroke=\"#000\"/><path d=\"m858.953 254.824c0 7.754-6.285 14.039-14.039 14.039s-14.039-6.285-14.039-14.039 6.285-14.039 14.039-14.039 14.039 6.285 14.039 14.039z\" stroke=\"#000\"/><path d=\"m493.91 254.824h698.5\" stroke=\"#000\"/><path d=\"m974.785 353.105c0 7.754-6.285 14.04-14.039 14.04s-14.039-6.286-14.039-14.04c0-7.753 6.285-14.039 14.039-14.039s14.039 6.286 14.039 14.039z\" stroke=\"#000\"/><path d=\"m651.859 2.10156 624.791 702.01144\" stroke=\"#000\"/><path d=\"m1933.04 784.844c0 7.754-6.29 14.039-14.05 14.039-7.75 0-14.04-6.285-14.04-14.039s6.29-14.039 14.04-14.039c7.76 0 14.05 6.285 14.05 14.039z\" stroke=\"#000\"/><path d=\"m1567.99 735.703 702.01 98.281\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 132.602 708.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 171.602 708.801)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 483 708.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 522 708.801)\"><tspan x=\"0 68.219673 103.37982 138.41968\" y=\"0\">1123</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 909.602 69.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 948.602 69.199)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 909.602 420.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 948.602 420.199)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-69.960197\">1</tspan><tspan x=\"-3.9\" y=\"-105.12\">2</tspan><tspan x=\"-3.9\" y=\"-140.1602\">3</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 1989.602 720.801)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-110.28\" y=\"-120.72\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(-3-2x\\right)\\left(x-4\\right)}{\\left(2x+3\\right)^{2}+1}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -2.42 &nbsp; </td><td> &nbsp; -2.04 &nbsp; </td><td> &nbsp; -1.51 &nbsp; </td><td> &nbsp; -1.50 &nbsp; </td><td> &nbsp; -1.04 &nbsp; </td><td> &nbsp; -.69 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; -2.68 &nbsp; </td><td> &nbsp; -3.01 &nbsp; </td><td> &nbsp; -.16 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 2.51 &nbsp; </td><td> &nbsp; 2.09 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; -1.17 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 11.03 &nbsp; </td><td> &nbsp; 11.00 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -1.60 &nbsp; </td><td> &nbsp; -.09 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 9.13 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -4.00 &nbsp; </td><td> &nbsp; -13.13 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .03 </td></tr></table>\n\n<br><svg height=\"281.54666\" viewBox=\"0 0 302.69333 281.54666\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 281.54667)\"><path d=\"m79.1797 57.4688v1916.9712\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m353.031 57.4688v1916.9712\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m626.883 57.4688v1916.9712\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1174.59 57.4688v1916.9712\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1448.44 57.4688v1916.9712\" 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0-10.953-4.91-10.953-10.96s4.902-10.95 10.953-10.95c6.05 0 10.953 4.9 10.953 10.95z\" stroke=\"#000\"/><path d=\"m342.078 1840.25h547.703\" stroke=\"#000\"/><path d=\"m722.73 1725.23c0 6.05-4.902 10.96-10.953 10.96-6.05 0-10.953-4.91-10.953-10.96s4.903-10.95 10.953-10.95c6.051 0 10.953 4.9 10.953 10.95z\" stroke=\"#000\"/><path d=\"m884.305 1451.38-342.317 547.71\" stroke=\"#000\"/><path d=\"m2007.1 1152.88c0 6.05-4.9 10.96-10.95 10.96s-10.96-4.91-10.96-10.96 4.91-10.95 10.96-10.95 10.95 4.9 10.95 10.95z\" stroke=\"#000\"/><path d=\"m1722.29 1177.53 547.71-49.3\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 47.3984 1080.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 86.3984 1080.2)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 321.0004 1080.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 360.0004 1080.2)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 594.6024 1080.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 633.6024 1080.2)\"><tspan x=\"0 52.859776 80.219925 107.57967 135.05977\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 942.0004 43.4)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 981.0004 43.4)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 942.0004 317.603)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 981.0004 317.603)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 942.0004 591.201)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 981.0004 591.201)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 942.0004 864.803)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 981.0004 864.803)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-54.599998\">1</tspan><tspan x=\"-3.9\" y=\"-81.959801\">2</tspan><tspan x=\"-3.9\" y=\"-109.3801\">3</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2055.6004 1088.604)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-113.4\" y=\"-96.479698\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(2x+2\\right)\\left(x-4\\right)}{\\left(2x+1\\right)^{2}+2}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -3.09 &nbsp; </td><td> &nbsp; -2.17 &nbsp; </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; -.68 &nbsp; </td><td> &nbsp; -.20 &nbsp; </td><td> &nbsp; .21 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 1.02 &nbsp; </td><td> &nbsp; 1.09 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -1.37 &nbsp; </td><td> &nbsp; -2.84 &nbsp; </td><td> &nbsp; -2.27 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; .10 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -3.33 &nbsp; </td><td> &nbsp; -5.04 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.94 &nbsp; </td><td> &nbsp; .12 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.36 &nbsp; </td><td> &nbsp; -7.55 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 11.36 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.05 </td></tr></table>\n\n<br><svg height=\"191.32001\" viewBox=\"0 0 302.69333 191.32001\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 191.32)\"><path d=\"m51.793 68.6484v1232.3316\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m298.262 68.6484v1232.3316\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m544.727 68.6484v1232.3316\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m791.195 68.6484v1232.3316\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1284.13 68.6484v1232.3316\" 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d=\"m865.137 561.582-147.883 492.938\" stroke=\"#000\"/><path d=\"m879.922 470.387c0 5.445-4.414 9.859-9.856 9.859-5.445 0-9.859-4.414-9.859-9.859 0-5.442 4.414-9.856 9.859-9.856 5.442 0 9.856 4.414 9.856 9.856z\" stroke=\"#000\"/><path d=\"m919.359 223.922-98.589 492.933\" stroke=\"#000\"/><path d=\"m998.227 108.082c0 5.445-4.414 9.859-9.856 9.859-5.445 0-9.859-4.414-9.859-9.859s4.414-9.8593 9.859-9.8593c5.442 0 9.856 4.4143 9.856 9.8593z\" stroke=\"#000\"/><path d=\"m741.902 108.082h490.468\" stroke=\"#000\"/><path d=\"m1099.28 248.566c0 5.446-4.41 9.86-9.86 9.86-5.44 0-9.86-4.414-9.86-9.86 0-5.445 4.42-9.855 9.86-9.855 5.45 0 9.86 4.41 9.86 9.855z\" stroke=\"#000\"/><path d=\"m963.723 2.10156 251.397 492.93344\" stroke=\"#000\"/><path d=\"m2033.39 808.047c0 5.445-4.41 9.859-9.86 9.859-5.44 0-9.86-4.414-9.86-9.859 0-5.442 4.42-9.856 9.86-9.856 5.45 0 9.86 4.414 9.86 9.856z\" stroke=\"#000\"/><path d=\"m1777.07 778.473 492.93 59.152\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 19.8008 736.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 58.8008 736.398)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 266.9998 736.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 305.9998 736.398)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 512.9998 736.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 551.9998 736.398)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 758.9998 736.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 797.9998 736.398)\"><tspan x=\"0 47.339825 72.060127 96.660126 121.26012\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1077.6018 54.8)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1116.6018 54.8)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1077.6018 301.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1116.6018 301.398)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1077.6018 547.398)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1116.6018 547.398)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-49.080101\">1</tspan><tspan x=\"-3.9\" y=\"-73.800003\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2079.6018 743.601)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-102.12\" y=\"-63.239799\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(2x-1\\right)\\left(-3-x\\right)}{\\left(2x-1\\right)^{2}+1}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -3.00 &nbsp; </td><td> &nbsp; -.27 &nbsp; </td><td> &nbsp; .06 &nbsp; </td><td> &nbsp; .50 &nbsp; </td><td> &nbsp; .52 &nbsp; </td><td> &nbsp; 1.07 &nbsp; </td><td> &nbsp; 1.46 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.23 &nbsp; </td><td> &nbsp; 1.51 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.16 &nbsp; </td><td> &nbsp; -2.01 &nbsp; </td><td> &nbsp; -1.82 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; .14 &nbsp; </td><td> &nbsp; 1.11 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -7.00 &nbsp; </td><td> &nbsp; -7.04 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .68 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; .07 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -9.21 &nbsp; </td><td> &nbsp; -4.00 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 5.21 &nbsp; </td><td> &nbsp; .00 </td></tr></table>\n\n<br><svg height=\"284.42667\" viewBox=\"0 0 302.69333 284.42667\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 284.42667)\"><path d=\"m190.227 78.9922v1902.2578\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m570.68 78.9922v1902.2578\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m951.133 78.9922v1902.2578\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1712.04 78.9922v1902.2578\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2092.49 78.9922v1902.2578\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m190.227 78.9922h1902.263\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m190.227 459.445h1902.263\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m190.227 839.898h1902.263\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m190.227 1600.8h1902.263\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m190.227 1981.25h1902.263\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m190.227 1235.57v-30.44\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m151.922 1132.52h76.609v49.21h-76.609z\" fill=\"#fff\"/><path d=\"m151.922 1132.52h76.609v49.21h-76.609z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m570.68 1235.57v-30.44\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m532.375 1132.52h76.605v49.21h-76.605z\" fill=\"#fff\"/><path d=\"m532.375 1132.52h76.605v49.21h-76.605z\" 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fill=\"#fff\"/><path d=\"m1339.76 2042.69h78.33v88.18h-78.33z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2093.59 1220.35h-1979.453\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2168.58 1220.35-74.99 20.1v-40.2z\"/><path d=\"m2168.58 1220.35-74.99 20.1v-40.2z\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1331.59 1982.36v-1979.46156\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1331.59 2057.35-20.1-74.99h40.19z\"/><g fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-miterlimit=\"10\" stroke-width=\"5\"><path d=\"m1331.59 2057.35-20.1-74.99h40.19z\" stroke=\"#000\"/><path d=\"m190.227 1220.35 19.023 2.7 19.023 2.78 19.02 2.85 19.023 2.94 19.024 3.02 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19.02 12.887 19.03 12.957 19.02 12.867 19.02 12.668 19.02 12.387 19.03 12.055 19.02 11.683 19.02 11.293 19.02 10.895 19.03 10.488 19.02 10.098 19.02 9.703\" stroke=\"#000\" stroke-dasharray=\"40.3867 40.3867\"/><path d=\"m205.445 1220.35c0 8.4-6.812 15.22-15.218 15.22-8.407 0-15.219-6.82-15.219-15.22s6.812-15.22 15.219-15.22c8.406 0 15.218 6.82 15.218 15.22z\" stroke=\"#000\"/><path d=\"m-190.227 1167.09 760.907 106.52\" stroke=\"#000\"/><path d=\"m1244.08 1688.31c0 8.4-6.81 15.21-15.22 15.21-8.4 0-15.22-6.81-15.22-15.21 0-8.41 6.82-15.22 15.22-15.22 8.41 0 15.22 6.81 15.22 15.22z\" stroke=\"#000\"/><path d=\"m886.457 1307.86 677.203 760.9\" stroke=\"#000\"/><path d=\"m1369.63 1794.83c0 8.41-6.81 15.22-15.22 15.22-8.4 0-15.21-6.81-15.21-15.22 0-8.4 6.81-15.21 15.21-15.21 8.41 0 15.22 6.81 15.22 15.21z\" stroke=\"#000\"/><path d=\"m977.766 1794.83h757.104\" stroke=\"#000\"/><path d=\"m1537.03 1220.35c0 8.4-6.82 15.22-15.22 15.22s-15.22-6.82-15.22-15.22 6.82-15.22 15.22-15.22 15.22 6.82 15.22 15.22z\" stroke=\"#000\"/><path d=\"m1575.07 839.898-110.33 760.902\" stroke=\"#000\"/><path d=\"m1544.64 1159.48c0 8.4-6.82 15.22-15.22 15.22s-15.22-6.82-15.22-15.22c0-8.41 6.82-15.22 15.22-15.22s15.22 6.81 15.22 15.22z\" stroke=\"#000\"/><path d=\"m1582.68 779.023-106.52 757.107\" stroke=\"#000\"/><path d=\"m1753.89 455.641c0 8.402-6.82 15.214-15.22 15.214s-15.22-6.812-15.22-15.214c0-8.407 6.82-15.219 15.22-15.219s15.22 6.812 15.22 15.219z\" stroke=\"#000\"/><path d=\"m1358.22 455.641h760.91\" stroke=\"#000\"/><path d=\"m1902.27 527.926c0 8.402-6.82 15.219-15.22 15.219-8.41 0-15.22-6.817-15.22-15.219 0-8.406 6.81-15.219 15.22-15.219 8.4 0 15.22 6.813 15.22 15.219z\" stroke=\"#000\"/><path d=\"m1506.59 269.219 760.91 521.219\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 159 1143.4)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 198 1143.4)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 539.398 1143.4)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 578.398 1143.4)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 919.8 1143.4)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 958.8 1143.4)\"><tspan x=\"0 74.100121 112.13998\" y=\"0\">112</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1376.398 65.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1415.398 65.2)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1376.398 445.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1415.398 445.602)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1376.398 826)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1415.398 826)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-75.900002\">1</tspan><tspan x=\"-3.9\" y=\"-113.9398\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2167.199 1156)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-81.480103\" y=\"-91.919899\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(-2-2x\\right)\\left(x-1\\right)}{\\left(2x+1\\right)^{2}+1}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -3.70 &nbsp; </td><td> &nbsp; -2.61 &nbsp; </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; -.69 &nbsp; </td><td> &nbsp; -.38 &nbsp; </td><td> &nbsp; -.09 &nbsp; </td><td> &nbsp; 1.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; -.60 &nbsp; </td><td> &nbsp; -.61 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .90 &nbsp; </td><td> &nbsp; 1.61 &nbsp; </td><td> &nbsp; 1.20 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; -.01 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; 3.62 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -2.11 &nbsp; </td><td> &nbsp; -.40 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; .04 &nbsp; </td><td> &nbsp; 6.00 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -16.04 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .56 </td></tr></table>\n\n<br><svg height=\"168.88\" viewBox=\"0 0 302.35999 168.88\" width=\"302.35999\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 168.88)\"><path d=\"m174.586 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stroke-width=\"5\"><path d=\"m1569.66 1187.91-20.09-74.97h40.18z\" stroke=\"#000\"/><path d=\"m174.586 211.359 17.437-.277 17.438-.281 17.437-.285 17.442-.282 17.437-.285 17.438-.285 17.437-.281 17.442-.285 17.437-.285 17.438-.278 17.437-.281 17.442-.277 17.437-.27 17.438-.269 17.437-.262 17.442-.254 17.437-.25 17.438-.238 17.437-.227 17.441-.211 17.438-.199 17.437-.18 17.438-.16 17.441-.141 17.438-.109 17.437-.082 17.438-.047 17.441-.004 17.438.039 17.437.094 17.438.152 17.441.219 17.438.297 17.437.391 17.438.488 17.441.609 17.438.742 17.437.899 17.438 1.074 17.437 1.281 17.442 1.52 17.437 1.797 17.438 2.113 17.437 2.481 17.441 2.914 17.438 3.418 17.437 4.003 17.439 4.688 17.44 5.5 17.44 6.445 17.44 7.567 17.43 8.883 17.44 10.449 17.44 12.289 17.44 14.469 17.44 17.039 17.44 20.062 17.44 23.594 17.43 27.68 17.44 32.351 17.44 37.574 17.44 43.239 17.44 49.101 17.43 54.731 17.45 59.496 17.43 62.539 17.44 62.89 17.44 59.688 17.44 52.461 17.44 41.437 17.43 27.625 17.44 12.618 17.44-1.848 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d=\"m1569.66 560.129 697.54-279.016\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 142.398 345.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 181.398 345.199)\"><tspan x=\"0\" y=\"0\">4</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 491.601 345.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 530.601 345.199)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 840.8 345.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 879.8 345.199)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1189.999 345.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1228.999 345.199)\"><tspan x=\"0 67.739975\" y=\"0\">11</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1614.198 57.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1653.198 57.801)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-69.599998\">1</tspan><tspan x=\"-3.9\" y=\"-104.5199\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 1988.6 357.199)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-39.720299\" y=\"-85.080101\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(4-2x\\right)\\left(2-x\\right)}{\\left(2x-1\\right)^{2}+2}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -.25 &nbsp; </td><td> &nbsp; .16 &nbsp; </td><td> &nbsp; .66 &nbsp; </td><td> &nbsp; 2.00 &nbsp; </td><td> &nbsp; 2.83 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 2.37 &nbsp; </td><td> &nbsp; 2.75 &nbsp; </td><td> &nbsp; 1.68 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .05 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; 1.24 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -3.59 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .09 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -7.36 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; .36 &nbsp; </td><td> &nbsp; 0.00 </td></tr></table>\n\n<br><svg height=\"215.33333\" viewBox=\"0 0 303.02667 215.33333\" width=\"303.02667\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 215.33333)\"><path d=\"m92.4375 93.7266v1352.0934\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m993.832 93.7266v1352.0934\" 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stroke-miterlimit=\"10\" stroke-width=\"5\"><path d=\"m543.133 1535.95-20.09-74.97h40.18z\" stroke=\"#000\"/><path d=\"m92.4375 831.23 18.0275 12.766 18.027 13.285 18.031 13.824 18.028 14.383 18.027 14.965 18.027 15.563 18.028 16.183 18.027 16.813 18.028 17.457 18.027 18.109 18.031 18.762 18.027 19.4 18.028 20.03 18.027 20.62 18.027 21.18 18.028 21.66 18.027 22.05 18.031 22.33 18.028 22.45 18.027 22.37 18.027 22.05 18.028 21.43 18.027 20.46 18.027 19.06 18.028 17.15 18.031 14.7 18.027 11.6 18.028 7.83 18.027 3.36 18.027-1.84 18.028-7.69 18.027-14.15 18.027-21.03 18.032-28.16 18.027-35.31 18.027-42.19 18.028-48.52 18.027-54.04 18.027-58.53 18.028-61.84 18.027-63.879 18.031-64.661 18.028-64.253 18.027-62.793 18.027-60.454 18.028-57.429 18.027-53.906 18.027-50.071 18.028-46.078 18.031-42.055 18.028-38.109 18.03-34.312 18.02-30.723 18.03-27.371 18.03-24.27 18.03-21.433 18.03-18.852 18.02-16.516 18.03-14.417 18.03-12.532 18.03-10.851 18.02-9.356 18.03-8.015 18.03-6.836 18.03-5.785 18.03-4.856 18.02-4.035 18.03-3.309 18.03-2.6677 18.03-2.1015 18.02-1.6055 18.03-1.1602 18.03-.7773 18.03-.4375 18.03-.1367 18.02.125 18.03.3554 18.03.5586 18.03.7344 18.02.8867 18.04 1.0196 18.02 1.1367 18.03 1.2383 18.03 1.3207 18.02 1.398 18.03 1.461 18.03 1.512 18.03 1.558 18.03 1.594 18.03 1.625 18.02 1.648 18.03 1.668 18.03 1.68 18.02 1.692 18.03 1.699 18.03 1.699 18.03 1.699 18.03 1.699 18.03 1.692 18.02 1.687\" stroke=\"#000\" stroke-dasharray=\"39.5011 39.5011\"/><path d=\"m448.488 1161.88c0 9.95-8.07 18.03-18.027 18.03s-18.027-8.08-18.027-18.03c0-9.96 8.07-18.03 18.027-18.03s18.027 8.07 18.027 18.03z\" stroke=\"#000\"/><path d=\"m69.9023 711.18 716.6097 901.39\" stroke=\"#000\"/><path d=\"m633.273 1333.14c0 9.96-8.07 18.03-18.027 18.03s-18.027-8.07-18.027-18.03 8.07-18.03 18.027-18.03 18.027 8.07 18.027 18.03z\" stroke=\"#000\"/><path d=\"m169.059 1333.14h896.881\" stroke=\"#000\"/><path d=\"m858.621 850.895c0 9.957-8.07 18.031-18.027 18.031s-18.028-8.074-18.028-18.031c0-9.954 8.071-18.028 18.028-18.028s18.027 8.074 18.027 18.028z\" stroke=\"#000\"/><path d=\"m966.789 400.199-252.391 901.391\" stroke=\"#000\"/><path d=\"m1462.55 93.7266c0 9.9574-8.07 18.0274-18.02 18.0274-9.96 0-18.03-8.07-18.03-18.0274 0-9.9571 8.07-18.0274 18.03-18.0274 9.95 0 18.02 8.0703 18.02 18.0274z\" stroke=\"#000\"/><path d=\"m993.832 93.7266h901.388\" stroke=\"#000\"/><path d=\"m1836.63 116.262c0 9.957-8.07 18.027-18.02 18.027-9.96 0-18.03-8.07-18.03-18.027s8.07-18.0276 18.03-18.0276c9.95 0 18.02 8.0706 18.02 18.0276z\" stroke=\"#000\"/><path d=\"m1367.91 80.207 901.39 81.125\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 60.3984 13.8008)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 99.3984 13.8008)\"><tspan x=\"0 88.260025 133.26003 178.37993\" y=\"0\">1123</tspan><tspan x=\"49.200001\" y=\"-51.480099\">1</tspan><tspan x=\"49.200001\" y=\"-96.539902\">2</tspan><tspan x=\"49.200001\" y=\"-141.65981\">3</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 1979.7984 29.3988)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-141.48\" y=\"-152.03999\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(2x+4\\right)\\left(1-x\\right)}{\\left(2x-2\\right)^{2}+2}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -.03 &nbsp; </td><td> &nbsp; .44 &nbsp; </td><td> &nbsp; 1.00 &nbsp; </td><td> &nbsp; 1.05 &nbsp; </td><td> &nbsp; 1.89 &nbsp; </td><td> &nbsp; 2.47 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .64 &nbsp; </td><td> &nbsp; .83 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.16 &nbsp; </td><td> &nbsp; -1.33 &nbsp; </td><td> &nbsp; -1.23 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; .15 &nbsp; </td><td> &nbsp; .55 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -3.00 &nbsp; </td><td> &nbsp; -3.05 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; .24 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; .09 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -3.29 &nbsp; </td><td> &nbsp; -2.00 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 1.29 &nbsp; </td><td> &nbsp; .00 </td></tr></table>\n\n<br><svg height=\"182.67999\" viewBox=\"0 0 302.69333 182.67999\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 182.68)\"><path d=\"m189.906 78.4648v1139.4452\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m569.723 78.4648v1139.4452\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1329.36 78.4648v1139.4452\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1709.17 78.4648v1139.4452\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2088.99 78.4648v1139.4452\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m189.906 78.4648h1899.084\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m189.906 458.277h1899.084\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m189.906 1217.91h1899.084\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m189.906 853.289v-30.387\" 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d=\"m205.102 838.094c0 8.39-6.805 15.195-15.196 15.195-8.39 0-15.191-6.805-15.191-15.195 0-8.391 6.801-15.192 15.191-15.192 8.391 0 15.196 6.801 15.196 15.192z\" stroke=\"#000\"/><path d=\"m-189.906 781.121 759.629 113.945\" stroke=\"#000\"/><path d=\"m953.336 1081.18c0 8.39-6.801 15.19-15.191 15.19-8.391 0-15.192-6.8-15.192-15.19s6.801-15.2 15.192-15.2c8.39 0 15.191 6.81 15.191 15.2z\" stroke=\"#000\"/><path d=\"m558.328 872.277 755.832 421.603\" stroke=\"#000\"/><path d=\"m1131.85 1153.34c0 8.39-6.8 15.2-15.19 15.2s-15.2-6.81-15.2-15.2 6.81-15.19 15.2-15.19 15.19 6.8 15.19 15.19z\" stroke=\"#000\"/><path d=\"m740.641 1153.34h755.829\" stroke=\"#000\"/><path d=\"m1344.55 838.094c0 8.39-6.8 15.195-15.19 15.195-8.4 0-15.2-6.805-15.2-15.195 0-8.391 6.8-15.192 15.2-15.192 8.39 0 15.19 6.801 15.19 15.192z\" stroke=\"#000\"/><path d=\"m1454.7 458.277-254.48 759.633\" stroke=\"#000\"/><path d=\"m1363.54 777.324c0 8.391-6.8 15.192-15.19 15.192s-15.2-6.801-15.2-15.192c0-8.39 6.81-15.191 15.2-15.191s15.19 6.801 15.19 15.191z\" stroke=\"#000\"/><path d=\"m1473.68 397.508-250.67 755.832\" stroke=\"#000\"/><path d=\"m1682.58 332.941c0 8.391-6.8 15.192-15.19 15.192s-15.19-6.801-15.19-15.192c0-8.39 6.8-15.195 15.19-15.195s15.19 6.805 15.19 15.195z\" stroke=\"#000\"/><path d=\"m1287.57 332.941h759.64\" stroke=\"#000\"/><path d=\"m1902.88 370.922c0 8.391-6.81 15.191-15.2 15.191s-15.19-6.8-15.19-15.191 6.8-15.192 15.19-15.192 15.2 6.801 15.2 15.192z\" stroke=\"#000\"/><path d=\"m1507.87 275.969 759.63 189.906\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 157.801 760.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 196.801 760.801)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 538.199 760.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 577.199 760.801)\"><tspan x=\"0 73.980072 111.89997 149.94022\" y=\"0\">1123</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 994.801 64.199)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1033.801 64.199)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 994.801 444.601)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 1033.801 444.601)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-75.719902\">1</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2163.601 773.999)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-119.28\" y=\"-53.760201\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(2x+1\\right)\\left(x-4\\right)}{\\left(2x+1\\right)^{2}+1}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -1.44 &nbsp; </td><td> &nbsp; -1.05 &nbsp; </td><td> &nbsp; -.51 &nbsp; </td><td> &nbsp; -.50 &nbsp; </td><td> &nbsp; -.05 &nbsp; </td><td> &nbsp; .29 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 2.25 &nbsp; </td><td> &nbsp; 2.51 &nbsp; </td><td> &nbsp; .16 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -2.01 &nbsp; </td><td> &nbsp; -1.66 &nbsp; </td><td> &nbsp; 0.00 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; .92 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -9.03 &nbsp; </td><td> &nbsp; -9.00 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 1.36 &nbsp; </td><td> &nbsp; .10 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -7.16 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 11.16 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -.04 </td></tr></table>\n\n<br><svg height=\"271.17334\" viewBox=\"0 0 302.69333 271.17334\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 271.17333)\"><path d=\"m136.598 63.0547v1828.6253\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m441.371 63.0547v1828.6253\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1050.91 63.0547v1828.6253\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1355.68 63.0547v1828.6253\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1660.46 63.0547v1828.6253\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1965.23 63.0547v1828.6253\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 63.0547h1828.632\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 367.824h1828.632\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 672.598h1828.632\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 1282.14h1828.632\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 1586.91h1828.632\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 1891.68h1828.632\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m136.598 989.559v-24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m98.2969 892.563h76.6051v49.21h-76.6051z\" fill=\"#fff\"/><path d=\"m98.2969 892.563h76.6051v49.21h-76.6051z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m441.371 989.559v-24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m403.066 892.563h76.606v49.21h-76.606z\" fill=\"#fff\"/><path d=\"m403.066 892.563h76.606v49.21h-76.606z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m746.141 989.559v-24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1050.91 989.559v-24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1031.98 896.715h37.87v45.058h-37.87z\" fill=\"#fff\"/><path d=\"m1031.98 896.715h37.87v45.058h-37.87z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1355.68 989.559v-24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1336.75 896.715h37.87v45.058h-37.87z\" fill=\"#fff\"/><path d=\"m1336.75 896.715h37.87v45.058h-37.87z\" 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style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m781.738 38.4492h76.606v49.211h-76.606z\" fill=\"#fff\"/><path d=\"m781.738 38.4492h76.606v49.211h-76.606z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m733.953 367.824h24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m781.738 343.219h76.606v49.211h-76.606z\" fill=\"#fff\"/><path d=\"m781.738 343.219h76.606v49.211h-76.606z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m733.953 672.598h24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m781.738 647.992h76.606v49.211h-76.606z\" fill=\"#fff\"/><path d=\"m781.738 647.992h76.606v49.211h-76.606z\" 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style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m733.953 1891.68h24.379\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m781.738 1869.15h37.864v45.06h-37.864z\" fill=\"#fff\"/><path d=\"m781.738 1869.15h37.864v45.06h-37.864z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2016.07 900.387h82.85v68.812h-82.85z\" fill=\"#fff\"/><path d=\"m2016.07 900.387h82.85v68.812h-82.85z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m754.313 1942.52h78.335v88.19h-78.335z\" fill=\"#fff\"/><path d=\"m754.313 1942.52h78.335v88.19h-78.335z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1951.19 977.367h-1875.5455\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2026.18 977.367-74.99 20.098v-40.192z\"/><path d=\"m2026.18 977.367-74.99 20.098v-40.192z\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m746.141 1877.64v-1875.53844\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m746.141 1952.64-20.094-75h40.191z\"/><g fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-miterlimit=\"10\" stroke-width=\"5\"><path d=\"m746.141 1952.64-20.094-75h40.191z\" stroke=\"#000\"/><path d=\"m136.598 1525.96 18.289 12.37 18.285 12.99 18.285 13.63 18.289 14.26 18.285 14.92 18.285 15.52 18.286 16.08 18.289 16.54 18.285 16.86 18.285 16.91 18.289 16.63 18.285 15.81 18.285 14.24 18.285 11.6 18.29 7.48 18.285 1.33 18.285-7.51 18.289-19.76 18.285-36.14 18.285-56.95 18.285-81.83 18.289-109 18.286-135.05 18.285-155.12 18.289-164.403 18.285-160.074 18.285-142.852 18.289-116.671 18.285-86.899 18.286-58.226 18.285-33.579 18.289-14.101 18.285.324 18.285 10.414 18.289 17.106 18.285 21.25 18.285 23.574 18.286 24.637 18.289 24.835 18.285 24.481 18.285 23.766 18.289 22.839 18.285 21.797 18.285 20.703 18.285 19.61 18.29 18.527 18.285 17.492 18.285 16.504 18.29 15.567 18.28 14.683 18.29 13.86 18.29 13.089 18.28 12.368 18.29 11.699 18.28 11.074 18.29 10.492 18.29 9.949 18.28 9.446 18.29 8.972 18.29 8.536 18.28 8.121 18.29 7.742 18.29 7.379 18.28 7.047 18.29 6.73 18.29 6.434 18.28 6.16 18.29 5.898 18.28 5.653 18.29 5.425 18.29 5.204 18.28 5 18.29 4.808 18.29 4.625 18.28 4.449 18.29 4.289 18.28 4.133 18.29 3.985 18.28 3.843 18.29 3.715 18.29 3.586 18.28 3.469 18.29 3.351 18.29 3.247 18.28 3.14 18.29 3.043 18.29 2.949 18.28 2.86 18.29 2.769 18.29 2.692 18.28 2.609 18.29 2.535 18.28 2.465 18.29 2.395 18.29 2.328 18.28 2.261 18.29 2.204 18.29 2.144 18.28 2.09 18.29 2.031\" stroke=\"#000\" stroke-dasharray=\"40.1064 40.1064\"/><path d=\"m319.461 1663.11c0 6.73-5.457 12.19-12.191 12.19-6.731 0-12.188-5.46-12.188-12.19 0-6.74 5.457-12.2 12.188-12.2 6.734 0 12.191 5.46 12.191 12.2z\" stroke=\"#000\"/><path d=\"m2.5 1379.67 609.543 563.83\" stroke=\"#000\"/><path d=\"m438.324 1742.34c0 6.74-5.461 12.2-12.191 12.2-6.735 0-12.192-5.46-12.192-12.2 0-6.73 5.457-12.18 12.192-12.18 6.73 0 12.191 5.45 12.191 12.18z\" stroke=\"#000\"/><path d=\"m121.359 1742.34h609.543\" stroke=\"#000\"/><path d=\"m602.898 1026.13c0 6.73-5.457 12.19-12.191 12.19-6.73 0-12.187-5.46-12.187-12.19s5.457-12.19 12.187-12.19c6.734 0 12.191 5.46 12.191 12.19z\" stroke=\"#000\"/><path d=\"m624.234 724.41-67.05 606.49\" stroke=\"#000\"/><path d=\"m605.949 977.367c0 6.735-5.461 12.192-12.191 12.192-6.735 0-12.192-5.457-12.192-12.192 0-6.73 5.457-12.187 12.192-12.187 6.73 0 12.191 5.457 12.191 12.187z\" stroke=\"#000\"/><path d=\"m630.328 672.598-70.098 609.542\" stroke=\"#000\"/><path d=\"m743.094 364.777c0 6.735-5.457 12.192-12.192 12.192-6.73 0-12.191-5.457-12.191-12.192 0-6.73 5.461-12.191 12.191-12.191 6.735 0 12.192 5.461 12.192 12.191z\" stroke=\"#000\"/><path d=\"m426.133 364.777h606.497\" stroke=\"#000\"/><path d=\"m846.715 471.449c0 6.731-5.457 12.192-12.188 12.192-6.734 0-12.191-5.461-12.191-12.192 0-6.734 5.457-12.191 12.191-12.191 6.731 0 12.188 5.457 12.188 12.191z\" stroke=\"#000\"/><path d=\"m615.09 166.676 444.97 609.543\" stroke=\"#000\"/><path d=\"m1977.42 977.367c0 6.735-5.46 12.192-12.19 12.192s-12.19-5.457-12.19-12.192c0-6.73 5.46-12.187 12.19-12.187s12.19 5.457 12.19 12.187z\" stroke=\"#000\"/><path d=\"m1660.46 946.891 609.54 60.959\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 105 903.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 144 903.801)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 409.801 903.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 448.801 903.801)\"><tspan x=\"0 58.980324 89.460022 119.94012 150.42023\" y=\"0\">11234</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 788.399 49.399)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 827.399 49.399)\"><tspan x=\"0\" y=\"0\">3</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 788.399 354.2)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 827.399 354.2)\"><tspan x=\"0\" y=\"0\">2</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 788.399 659.001)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 827.399 659.001)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-60.780102\">1</tspan><tspan x=\"-3.9\" y=\"-91.260201\">2</tspan><tspan x=\"-3.9\" y=\"-121.7399\">3</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2029.199 914.002)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-126.24\" y=\"-106.2\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(2-2x\\right)\\left(-1-x\\right)}{\\left(2x-2\\right)^{2}+1}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -1.00 &nbsp; </td><td> &nbsp; .27 &nbsp; </td><td> &nbsp; .60 &nbsp; </td><td> &nbsp; 1.00 &nbsp; </td><td> &nbsp; 1.04 &nbsp; </td><td> &nbsp; 1.64 &nbsp; </td><td> &nbsp; 2.05 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.59 &nbsp; </td><td> &nbsp; -.78 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; .16 &nbsp; </td><td> &nbsp; 1.28 &nbsp; </td><td> &nbsp; 1.18 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; -.23 &nbsp; </td><td> &nbsp; -.75 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; 4.08 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; -.32 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.20 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; 6.36 &nbsp; </td><td> &nbsp; 4.00 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -2.36 &nbsp; </td><td> &nbsp; .00 </td></tr></table>\n\n<br><svg height=\"238.03999\" viewBox=\"0 0 310.97333 238.03999\" width=\"310.97333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 238.04)\"><path d=\"m241.016 171.75v1447.29\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1205.88 171.75v1447.29\" 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style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2246.45 577.199h82.85v68.813h-82.85z\" fill=\"#fff\"/><path d=\"m2246.45 577.199h82.85v68.813h-82.85z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m731.617 1694.75h78.332v88.18h-78.332z\" fill=\"#fff\"/><path d=\"m731.617 1694.75h78.332v88.18h-78.332z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2192.23 654.18h-2047.703\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2267.22 654.18-74.99 20.093v-40.187z\"/><path d=\"m2267.22 654.18-74.99 20.093v-40.187z\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m723.445 1640.54v-1565.2744\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m723.445 1715.53-20.093-74.99h40.187z\"/><g fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-miterlimit=\"10\" stroke-width=\"5\"><path d=\"m723.445 1715.53-20.093-74.99h40.187z\" stroke=\"#000\"/><path d=\"m241.016 654.18 19.297-4.621 19.296-4.789 19.297-4.969 19.297-5.153 19.297-5.347 19.297-5.555 19.297-5.773 19.301-6 19.296-6.239 19.297-6.492 19.297-6.758 19.297-7.039 19.297-7.332 19.297-7.644 19.297-7.973 19.297-8.312 19.296-8.672 19.297-9.051 19.297-9.445 19.301-9.856 19.297-10.285 19.297-10.727 19.297-11.179 19.296-11.645 19.297-12.117 19.297-12.582 19.297-13.043 19.297-13.48 19.297-13.883 19.297-14.227 19.3-14.488 19.297-14.629 19.297-14.617 19.297-14.383 19.297-13.859 19.297-12.965 19.297-11.594 19.297-9.617 19.296-6.902 19.295-3.29 19.3 1.368 19.3 7.183 19.3 14.239 19.29 22.503 19.3 31.801 19.3 41.77 19.29 51.851 19.3 61.313 19.3 69.34 19.3 75.164 19.29 78.234 19.3 78.313 19.3 75.546 19.29 70.391 19.3 63.496 19.3 55.6 19.3 47.34 19.29 39.25 19.3 31.7 19.3 24.93 19.29 18.99 19.3 13.92 19.3 9.68 19.3 6.18 19.29 3.31 19.3 1.01 19.3-.83 19.3-2.28 19.29-3.41 19.3-4.26 19.3-4.93 19.29-5.4 19.3-5.75 19.3-5.99 19.29-6.12 19.3-6.21 19.3-6.22 19.3-6.2 19.3-6.14 19.29-6.06 19.3-5.96 19.3-5.85 19.29-5.71 19.3-5.59 19.3-5.44 19.29-5.3 19.3-5.16 19.3-5.02 19.29-4.87 19.31-4.74 19.29-4.6 19.3-4.47 19.3-4.33 19.29-4.21 19.3-4.09 19.3-3.96 19.29-3.85 19.3-3.74 19.3-3.62 19.29-3.53\" stroke=\"#000\" stroke-dasharray=\"39.4712 39.4712\"/><path d=\"m260.313 654.18c0 10.66-8.641 19.297-19.297 19.297-10.657 0-19.297-8.637-19.297-19.297 0-10.657 8.64-19.297 19.297-19.297 10.656 0 19.297 8.64 19.297 19.297z\" stroke=\"#000\"/><path d=\"m-241.414 765.141 964.859-221.918\" stroke=\"#000\"/><path d=\"m873 369.547c0 10.656-8.641 19.297-19.297 19.297-10.66 0-19.301-8.641-19.301-19.297s8.641-19.297 19.301-19.297c10.656 0 19.297 8.641 19.297 19.297z\" stroke=\"#000\"/><path d=\"m376.094 731.371 960.036-728.47256\" stroke=\"#000\"/><path d=\"m1032.2 277.887c0 10.656-8.64 19.297-19.3 19.297-10.65 0-19.295-8.641-19.295-19.297 0-10.66 8.645-19.297 19.295-19.297 10.66 0 19.3 8.637 19.3 19.297z\" stroke=\"#000\"/><path d=\"m535.297 277.887h960.033\" stroke=\"#000\"/><path d=\"m1225.17 654.18c0 10.66-8.64 19.297-19.29 19.297-10.66 0-19.3-8.637-19.3-19.297 0-10.657 8.64-19.297 19.3-19.297 10.65 0 19.29 8.64 19.29 19.297z\" stroke=\"#000\"/><path d=\"m1085.27 171.75 241.21 964.86\" stroke=\"#000\"/><path d=\"m1244.47 731.371c0 10.656-8.64 19.297-19.3 19.297-10.65 0-19.29-8.641-19.29-19.297 0-10.66 8.64-19.297 19.29-19.297 10.66 0 19.3 8.637 19.3 19.297z\" stroke=\"#000\"/><path d=\"m1104.57 253.766 236.39 960.034\" stroke=\"#000\"/><path d=\"m1533.93 1271.69c0 10.66-8.64 19.3-19.3 19.3s-19.3-8.64-19.3-19.3c0-10.65 8.64-19.3 19.3-19.3s19.3 8.65 19.3 19.3z\" stroke=\"#000\"/><path d=\"m1032.2 1271.69h964.86\" stroke=\"#000\"/><path d=\"m1731.72 1223.45c0 10.66-8.63 19.3-19.29 19.3s-19.3-8.64-19.3-19.3 8.64-19.3 19.3-19.3 19.29 8.64 19.29 19.3z\" stroke=\"#000\"/><path d=\"m1230 1377.83 964.86-313.58\" stroke=\"#000\"/></g><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 209.199 572.801)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 248.199 572.801)\"><tspan x=\"0 94.500122 142.74037 191.10013\" y=\"0\">1123</tspan></text><text font-family=\"CMSY10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 772.601 157.602)\"><tspan x=\"0\" y=\"0\">−</tspan></text><text font-family=\"CMR10\" font-size=\"4.98132\" transform=\"matrix(10 0 0 -10 811.601 157.602)\"><tspan x=\"0\" y=\"0\">1</tspan><tspan x=\"-3.9\" y=\"-96.300003\">1</tspan><tspan x=\"-3.9\" y=\"-144.53979\">2</tspan></text><text font-family=\"CMMI10\" font-size=\"9.96264\" transform=\"matrix(10 0 0 -10 2259.401 590.8)\"><tspan x=\"0\" y=\"0\">x</tspan><tspan x=\"-151.44\" y=\"-113.64\">y</tspan></text></g></svg>\n"], ["$\\displaystyle f(x) = \\frac{\\left(-3-2x\\right)\\left(1-x\\right)}{\\left(2x-3\\right)^{2}+2}$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> &nbsp; -1.50 &nbsp; </td><td> &nbsp; -.19 &nbsp; </td><td> &nbsp; .45 &nbsp; </td><td> &nbsp; 1.00 &nbsp; </td><td> &nbsp; 1.40 &nbsp; </td><td> &nbsp; 1.97 &nbsp; </td><td> &nbsp; 2.42 &nbsp; </td></tr>\n<tr><td>$f(x)$ &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.23 &nbsp; </td><td> &nbsp; -.33 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.17 &nbsp; </td><td> &nbsp; 2.33 &nbsp; </td><td> &nbsp; 2.06 </td></tr>\n<tr><td>$f'(x)$ &nbsp; </td><td> &nbsp; -.13 &nbsp; </td><td> &nbsp; -.21 &nbsp; </td><td> &nbsp; -.00 &nbsp; </td><td> &nbsp; 1.66 &nbsp; </td><td> &nbsp; 3.68 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; -.84 </td></tr>\n<tr><td>$f''(x)$ &nbsp; </td><td> &nbsp; -.06 &nbsp; </td><td> &nbsp; 0.00 &nbsp; </td><td> &nbsp; 1.04 &nbsp; </td><td> &nbsp; 5.77 &nbsp; </td><td> &nbsp; .00 &nbsp; </td><td> &nbsp; -5.04 &nbsp; </td><td> &nbsp; -.00 </td></tr></table>\n\n<br><svg height=\"235.17332\" viewBox=\"0 0 302.69333 235.17332\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 235.17333)\"><path d=\"m191.512 79.3047v1532.0953\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m574.535 79.3047v1532.0953\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1340.58 79.3047v1532.0953\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1723.61 79.3047v1532.0953\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2106.63 79.3047v1532.0953\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m191.512 79.3047h1915.118\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m191.512 845.352h1915.118\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m191.512 1228.38h1915.118\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m191.512 1611.4h1915.118\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m191.512 477.648v-30.64\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m153.207 374.391h76.609v49.211h-76.609z\" fill=\"#fff\"/><path d=\"m153.207 374.391h76.609v49.211h-76.609z\" 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style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1723.61 477.648v-30.64\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1704.67 378.543h37.87v45.059h-37.87z\" fill=\"#fff\"/><path d=\"m1704.67 378.543h37.87v45.059h-37.87z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2106.63 477.648v-30.64\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m2087.7 378.543h37.86v45.059h-37.86z\" fill=\"#fff\"/><path d=\"m2087.7 378.543h37.86v45.059h-37.86z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m942.238 79.3047h30.641\" 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<div style='font-size:12px;color:gray;'>ruby extremalstellen-von-polynom-3ten-grades.rb 4</div>
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