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Funktion: f(x) = x4 + x3 - 12x, Df = R, Wf = [-10.61; +∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 9120 | -3712 | 1140 | -233.99 | |
| -9.5 | 7401.6875 | -3170.75 | 1026 | -221.99 | |
| -9 | 5940 | -2685 | 918 | -209.99 | |
| -8.5 | 4707.9375 | -2251.75 | 816 | -198 | |
| -8 | 3680 | -1868 | 720 | -185.99 | |
| -7.5 | 2832.1875 | -1530.75 | 630 | -173.99 | |
| -7 | 2142 | -1237 | 546 | -161.99 | |
| -6.5 | 1588.4375 | -983.75 | 468 | -149.99 | |
| -6 | 1152 | -768 | 396 | -137.99 | |
| -5.5 | 814.6875 | -586.75 | 330 | -125.99 | |
| -5 | 560 | -437 | 270 | -113.99 | |
| -4.5 | 372.9375 | -315.75 | 216 | -101.99 | |
| -4 | 240 | -220 | 168 | -89.99 | |
| -3.5 | 149.1875 | -146.75 | 126 | -77.99 | |
| -3 | 90 | -93 | 90 | -65.99 | |
| -2.5 | 53.4375 | -55.75 | 60 | -53.99 | |
| -2 | 32 | -32 | 36 | -41.99 | |
| -1.5 | 19.6875 | -18.75 | 18 | -29.99 | |
| -1 | 12 | -13 | 6 | -17.99 | |
| -0.5 | 5.9375 | -11.75 | 0 | -5.99 | Wendepunkt W(-0.5|5.94) |
| 0 | 0 | -12 | 0 | 6.01 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
| 0.5 | -5.8125 | -10.75 | 6 | 18.01 | |
| 1 | -10 | -5 | 18 | 30.01 | |
| 1.23 | -10.6103 | 0 | 25.53 | 35.53 | Tiefpunkt T(1.23|-10.61) |
| 1.5 | -9.5625 | 8.25 | 36 | 42.01 | |
| 2 | 0 | 32 | 60 | 54.01 | Nullstelle N(2|0) |
| 2.5 | 24.6875 | 69.25 | 90 | 66.01 | |
| 3 | 72 | 123 | 126 | 78.01 | |
| 3.5 | 150.9375 | 196.25 | 168 | 90.01 | |
| 4 | 272 | 292 | 216 | 102.01 | |
| 4.5 | 447.1875 | 413.25 | 270 | 114.01 | |
| 5 | 690 | 563 | 330 | 126.01 | |
| 5.5 | 1015.4375 | 744.25 | 396 | 138.01 | |
| 6 | 1440 | 960 | 468 | 150.01 | |
| 6.5 | 1981.6875 | 1213.25 | 546 | 162.01 | |
| 7 | 2660 | 1507 | 630 | 174.01 | |
| 7.5 | 3495.9375 | 1844.25 | 720 | 186.01 | |
| 8 | 4512 | 2228 | 816 | 198.02 | |
| 8.5 | 5732.1875 | 2661.25 | 918 | 210.01 | |
| 9 | 7182 | 3147 | 1026 | 222.01 | |
| 9.5 | 8888.4375 | 3688.25 | 1140 | 234.02 | |
| 10 | 10880 | 4288 | 1260 | 246.02 | |
| 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