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Funktion: f(x) = 3x4 - 16x3, Df = R, Wf = [-256; +∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 46000 | -16800 | 4560 | -815.98 | |
| -9.5 | 38153.1875 | -14620.5 | 4161 | -780.01 | |
| -9 | 31347 | -12636 | 3780 | -743.99 | |
| -8.5 | 25486.1875 | -10837.5 | 3417 | -707.97 | |
| -8 | 20480 | -9216 | 3072 | -671.97 | |
| -7.5 | 16242.1875 | -7762.5 | 2745 | -635.98 | |
| -7 | 12691 | -6468 | 2436 | -599.98 | |
| -6.5 | 9749.1875 | -5323.5 | 2145 | -563.97 | |
| -6 | 7344 | -4320 | 1872 | -527.97 | |
| -5.5 | 5407.1875 | -3448.5 | 1617 | -491.97 | |
| -5 | 3875 | -2700 | 1380 | -455.96 | |
| -4.5 | 2688.1875 | -2065.5 | 1161 | -419.96 | |
| -4 | 1792 | -1536 | 960 | -383.96 | |
| -3.5 | 1136.1875 | -1102.5 | 777 | -347.96 | |
| -3 | 675 | -756 | 612 | -311.96 | |
| -2.5 | 367.1875 | -487.5 | 465 | -275.96 | |
| -2 | 176 | -288 | 336 | -239.96 | |
| -1.5 | 69.1875 | -148.5 | 225 | -203.96 | |
| -1 | 19 | -60 | 132 | -167.96 | |
| -0.5 | 2.1875 | -13.5 | 57 | -131.96 | |
| 0 | 0 | 0 | 0 | -95.96 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) = Sattelpunkt WS(0|0) |
| 0.5 | -1.8125 | -10.5 | -39 | -59.96 | |
| 1 | -13 | -36 | -60 | -23.96 | |
| 1.5 | -38.8125 | -67.5 | -63 | 12.04 | |
| 2 | -80 | -96 | -48 | 48.04 | |
| 2.5 | -132.8125 | -112.5 | -15 | 84.04 | |
| 2.666 | -151.6279 | -113.78 | 0 | 95.99 | Wendepunkt W(2.67|-151.63) |
| 3 | -189 | -108 | 36 | 120.04 | |
| 3.5 | -235.8125 | -73.5 | 105 | 156.04 | |
| 4 | -256 | 0 | 192 | 192.04 | Tiefpunkt T(4|-256) |
| 4.5 | -227.8125 | 121.5 | 297 | 228.04 | |
| 5 | -125 | 300 | 420 | 264.04 | |
| 5.333 | 0 | 454.94 | 511.9 | 288.01 | Nullstelle N(5.33|0) |
| 5.5 | 83.1875 | 544.5 | 561 | 300.04 | |
| 6 | 432 | 864 | 720 | 336.04 | |
| 6.5 | 961.1875 | 1267.5 | 897 | 372.03 | |
| 7 | 1715 | 1764 | 1092 | 408.04 | |
| 7.5 | 2742.1875 | 2362.5 | 1305 | 444.03 | |
| 8 | 4096 | 3072 | 1536 | 480.04 | |
| 8.5 | 5834.1875 | 3901.5 | 1785 | 516.05 | |
| 9 | 8019 | 4860 | 2052 | 552.03 | |
| 9.5 | 10717.1875 | 5956.5 | 2337 | 588.04 | |
| 10 | 14000 | 7200 | 2640 | 624.06 | |
| Graph: | |||||
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Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann