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Funktion: f(x) = x2·ln((x+2)x), Df = R\[-2; 0], Wf = R, reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -5 | 67.7013 | -40.41 | 12.3 | -0.92 | |
| -4.5 | 49.0125 | -34.38 | 11.8 | -1.12 | |
| -4 | 33.2711 | -28.64 | 11.16 | -1.5 | |
| -3.5 | 20.3133 | -23.27 | 10.21 | -2.51 | |
| -3 | 9.8875 | -18.59 | 8.2 | -6.71 | |
| -2.535 | 1.9581 | -16.09 | 0 | -43.43 | Wendepunkt W(-2.53|1.96) |
| -2.5 | 1.3946 | -16.12 | -1.55 | -53.64 | |
| -2.415 | 0 | -16.48 | -7.58 | -96.17 | Nullstelle N(-2.41|0) |
| -2 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -2 |
| 0 | 0 | - | - | - | Lücke L(0|0) |
| 0.095 | -0.0146 | -0.21 | 0 | 23.26 | Wendepunkt W(0.1|-0.01) |
| 0.25 | -0.036 | 0 | 2.28 | 10.3 | Tiefpunkt T(0.25|-0.04) |
| 0.41 | 0 | 0.47 | 3.63 | 6.93 | Nullstelle N(0.41|0) |
| 0.5 | 0.0558 | 0.82 | 4.21 | 5.93 | |
| 1 | 1.0986 | 3.53 | 6.42 | 3.4 | |
| 1.5 | 3.731 | 7.12 | 7.85 | 2.41 | |
| 2 | 8.3178 | 11.32 | 8.91 | 1.87 | |
| 2.5 | 15.1273 | 15.99 | 9.75 | 1.53 | |
| 3 | 24.3725 | 21.05 | 10.46 | 1.29 | |
| 3.5 | 36.2295 | 26.43 | 11.06 | 1.11 | |
| 4 | 50.8489 | 32.09 | 11.58 | 0.98 | |
| 4.5 | 68.3616 | 38 | 12.04 | 0.88 | |
| 5 | 88.8837 | 44.12 | 12.46 | 0.79 | |
| 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, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann