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Funktion: f(x) = -x2(x-4), Df = R, Wf = R, Polynom 3. Grades (Produktform), Funktion punktsymmetrisch zum Punkt W(1|0), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 1400 | -380 | 68 | -6 | |
| -9.5 | 1218.375 | -346.75 | 65 | -6 | |
| -9 | 1053 | -315 | 62 | -6 | |
| -8.5 | 903.125 | -284.75 | 59 | -6 | |
| -8 | 768 | -256 | 56 | -6 | |
| -7.5 | 646.875 | -228.75 | 53 | -6 | |
| -7 | 539 | -203 | 50 | -6 | |
| -6.5 | 443.625 | -178.75 | 47 | -6 | |
| -6 | 360 | -156 | 44 | -6 | |
| -5.5 | 287.375 | -134.75 | 41 | -6 | |
| -5 | 225 | -115 | 38 | -6 | |
| -4.5 | 172.125 | -96.75 | 35 | -6 | |
| -4 | 128 | -80 | 32 | -6 | |
| -3.5 | 91.875 | -64.75 | 29 | -6 | |
| -3 | 63 | -51 | 26 | -6 | |
| -2.5 | 40.625 | -38.75 | 23 | -6 | |
| -2 | 24 | -28 | 20 | -6 | |
| -1.5 | 12.375 | -18.75 | 17 | -6 | |
| -1 | 5 | -11 | 14 | -6 | |
| -0.5 | 1.125 | -4.75 | 11 | -6 | |
| 0 | 0 | 0 | 8 | -6 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
| 0.5 | 0.875 | 3.25 | 5 | -6 | |
| 1 | 3 | 5 | 2 | -6 | |
| 1.333 | 4.7407 | 5.33 | 0 | -6 | Wendepunkt W(1.33|4.74) |
| 1.5 | 5.625 | 5.25 | -1 | -6 | |
| 2 | 8 | 4 | -4 | -6 | |
| 2.5 | 9.375 | 1.25 | -7 | -6 | |
| 2.666 | 9.4815 | 0 | -8 | -6 | Hochpunkt H(2.67|9.48) |
| 3 | 9 | -3 | -10 | -6 | |
| 3.5 | 6.125 | -8.75 | -13 | -6 | |
| 4 | 0 | -16 | -16 | -6 | Nullstelle N(4|0) |
| 4.5 | -10.125 | -24.75 | -19 | -6 | |
| 5 | -25 | -35 | -22 | -6 | |
| 5.5 | -45.375 | -46.75 | -25 | -6 | |
| 6 | -72 | -60 | -28 | -6 | |
| 6.5 | -105.625 | -74.75 | -31 | -6 | |
| 7 | -147 | -91 | -34 | -6 | |
| 7.5 | -196.875 | -108.75 | -37 | -6 | |
| 8 | -256 | -128 | -40 | -6 | |
| 8.5 | -325.125 | -148.75 | -43 | -6 | |
| 9 | -405 | -171 | -46 | -6 | |
| 9.5 | -496.375 | -194.75 | -49 | -6 | |
| 10 | -600 | -220 | -52 | -6 | |
| 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