www.michael-buhlmann.de
Funktion: f(x) = -(x-2)2(x+3)2/20, Df = R, Wf = (-∞; 0], Polynom 4. Grades, Funktion achsensymmetrisch zur Senkrechten x = -0.5, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -352.8 | 159.6 | -52.9 | 11.4 | |
| -9.5 | -279.3781 | 134.55 | -47.35 | 10.8 | |
| -9 | -217.8 | 112.2 | -42.1 | 10.2 | |
| -8.5 | -166.7531 | 92.4 | -37.15 | 9.6 | |
| -8 | -125 | 75 | -32.5 | 9 | |
| -7.5 | -91.3781 | 59.85 | -28.15 | 8.4 | |
| -7 | -64.8 | 46.8 | -24.1 | 7.8 | |
| -6.5 | -44.2531 | 35.7 | -20.35 | 7.2 | |
| -6 | -28.8 | 26.4 | -16.9 | 6.6 | |
| -5.5 | -17.5781 | 18.75 | -13.75 | 6 | |
| -5 | -9.8 | 12.6 | -10.9 | 5.4 | |
| -4.5 | -4.7531 | 7.8 | -8.35 | 4.8 | |
| -4 | -1.8 | 4.2 | -6.1 | 4.2 | |
| -3.5 | -0.3781 | 1.65 | -4.15 | 3.6 | |
| -3 | 0 | 0 | -2.5 | 3 | Nullstelle N(-3|0) = Hochpunkt H(-3|0) |
| -2.5 | -0.2531 | -0.9 | -1.15 | 2.4 | |
| -2 | -0.8 | -1.2 | -0.1 | 1.8 | |
| -1.944 | -0.8673 | -1.2 | 0 | 1.73 | Wendepunkt W(-1.94|-0.87) |
| -1.5 | -1.3781 | -1.05 | 0.65 | 1.2 | |
| -1 | -1.8 | -0.6 | 1.1 | 0.6 | |
| -0.5 | -1.9531 | 0 | 1.25 | 0 | Tiefpunkt T(-0.5|-1.95) |
| 0 | -1.8 | 0.6 | 1.1 | -0.6 | Schnittpunkt Sy(0|-1.8) |
| 0.5 | -1.3781 | 1.05 | 0.65 | -1.2 | |
| 0.943 | -0.8685 | 1.2 | 0 | -1.73 | Wendepunkt W(0.94|-0.87) |
| 1 | -0.8 | 1.2 | -0.1 | -1.8 | |
| 1.5 | -0.2531 | 0.9 | -1.15 | -2.4 | |
| 2 | 0 | 0 | -2.5 | -3 | Nullstelle N(2|0) = Hochpunkt H(2|0) |
| 2.5 | -0.3781 | -1.65 | -4.15 | -3.6 | |
| 3 | -1.8 | -4.2 | -6.1 | -4.2 | |
| 3.5 | -4.7531 | -7.8 | -8.35 | -4.8 | |
| 4 | -9.8 | -12.6 | -10.9 | -5.4 | |
| 4.5 | -17.5781 | -18.75 | -13.75 | -6 | |
| 5 | -28.8 | -26.4 | -16.9 | -6.6 | |
| 5.5 | -44.2531 | -35.7 | -20.35 | -7.2 | |
| 6 | -64.8 | -46.8 | -24.1 | -7.8 | |
| 6.5 | -91.3781 | -59.85 | -28.15 | -8.4 | |
| 7 | -125 | -75 | -32.5 | -9 | |
| 7.5 | -166.7531 | -92.4 | -37.15 | -9.6 | |
| 8 | -217.8 | -112.2 | -42.1 | -10.2 | |
| 8.5 | -279.3781 | -134.55 | -47.35 | -10.8 | |
| 9 | -352.8 | -159.6 | -52.9 | -11.4 | |
| 9.5 | -439.4531 | -187.5 | -58.75 | -12 | |
| 10 | -540.8 | -218.4 | -64.9 | -12.6 | |
| Graph: | |||||
| |||||
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