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Funktion: f(x) = -x4 + x3 + x2 - x, Df = R, Wf = (-∞; 0.6197], Polynom 4. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -5 | -720 | 564 | -328 | 125.99 | |
| -4.5 | -476.4375 | 415.25 | -268 | 113.99 | |
| -4 | -300 | 295 | -214 | 101.99 | |
| -3.5 | -177.1875 | 200.25 | -166 | 89.99 | |
| -3 | -96 | 128 | -124 | 77.99 | |
| -2.5 | -45.9375 | 75.25 | -88 | 65.99 | |
| -2 | -18 | 39 | -58 | 53.99 | |
| -1.5 | -4.6875 | 16.25 | -34 | 41.99 | |
| -1 | 0 | 4 | -16 | 29.99 | Nullstelle N(-1|0) |
| -0.641 | 0.6197 | 0 | -6.78 | 21.37 | Hochpunkt H(-0.64|0.62) |
| -0.5 | 0.5625 | -0.75 | -4 | 17.99 | |
| -0.229 | 0.2667 | -1.25 | 0 | 11.48 | Wendepunkt W(-0.23|0.27) |
| 0 | 0 | -1 | 2 | 5.99 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.39 | -0.2017 | 0 | 2.51 | -3.37 | Tiefpunkt T(0.39|-0.2) |
| 0.5 | -0.1875 | 0.25 | 2 | -6.01 | |
| 0.728 | -0.0931 | 0.5 | 0 | -11.48 | Wendepunkt W(0.73|-0.09) |
| 1 | 0 | 0 | -4 | -18.01 | Hochpunkt H(1|0) |
| 1.5 | -0.9375 | -4.75 | -16 | -30.01 | |
| 2 | -6 | -17 | -34 | -42.01 | |
| 2.5 | -19.6875 | -39.75 | -58 | -54.01 | |
| 3 | -48 | -76 | -88 | -66.01 | |
| 3.5 | -98.4375 | -128.75 | -124 | -78.01 | |
| 4 | -180 | -201 | -166 | -90.01 | |
| 4.5 | -303.1875 | -295.75 | -214 | -102.01 | |
| 5 | -480 | -416 | -268 | -114.01 | |
| 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