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Funktion: f(x) = -x4/20 - x3/15 + x, Df = R, Wf = (-∞; 1.026], Polynom 4. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -5 | -27.9167 | 21 | -13 | 5.6 | |
| -4.5 | -18.9281 | 15.18 | -10.35 | 5 | |
| -4 | -12.5333 | 10.6 | -8 | 4.4 | |
| -3.5 | -8.1448 | 7.13 | -5.95 | 3.8 | |
| -3 | -5.25 | 4.6 | -4.2 | 3.2 | |
| -2.5 | -3.4115 | 2.88 | -2.75 | 2.6 | |
| -2 | -2.2667 | 1.8 | -1.6 | 2 | |
| -1.5 | -1.5281 | 1.23 | -0.75 | 1.4 | |
| -1 | -0.9833 | 1 | -0.2 | 0.8 | |
| -0.667 | -0.6571 | 0.97 | 0 | 0.4 | Wendepunkt W(-0.67|-0.66) |
| -0.5 | -0.4948 | 0.98 | 0.05 | 0.2 | |
| 0 | 0 | 1 | 0 | -0.4 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
| 0.5 | 0.4885 | 0.92 | -0.35 | -1 | |
| 1 | 0.8833 | 0.6 | -1 | -1.6 | |
| 1.433 | 1.026 | 0 | -1.81 | -2.12 | Hochpunkt H(1.43|1.03) |
| 1.5 | 1.0219 | -0.13 | -1.95 | -2.2 | |
| 2 | 0.6667 | -1.4 | -3.2 | -2.8 | |
| 2.334 | 0 | -2.63 | -4.2 | -3.2 | Nullstelle N(2.33|0) |
| 2.5 | -0.4948 | -3.38 | -4.75 | -3.4 | |
| 3 | -2.85 | -6.2 | -6.6 | -4 | |
| 3.5 | -6.8615 | -10.03 | -8.75 | -4.6 | |
| 4 | -13.0667 | -15 | -11.2 | -5.2 | |
| 4.5 | -22.0781 | -21.28 | -13.95 | -5.8 | |
| 5 | -34.5833 | -29 | -17 | -6.4 | |
| 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