, Df = R, Wf = R, Wurzelfunktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R, Wf = R, Wurzelfunktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 15.874 | -2.91 | 0.04 | -0.03 | |
| -9.5 | 14.4238 | -2.89 | 0.03 | -0.04 | |
| -9 | 12.9802 | -2.88 | 0 | -0.07 | Wendepunkt W(-9|12.98) |
| -8.5 | 11.5363 | -2.9 | -0.05 | -0.13 | |
| -8 | 10.0794 | -2.94 | -0.14 | -0.26 | |
| -7.5 | 8.5854 | -3.05 | -0.34 | -0.61 | |
| -7 | 7 | -3.33 | -0.89 | -1.95 | |
| -6.5 | 5.1591 | -4.23 | -3.53 | -13.54 | |
| -6 | 0 | Infinity | Infinity | Infinity | Nullstelle N(-6|0) = Wendepunkt W(-6|0) |
| -5.5 | -4.3654 | -2.12 | 4.94 | -14.67 | |
| -5 | -5 | -0.67 | 1.78 | -2.49 | |
| -4.5 | -5.1512 | 0 | 1.02 | -0.9 | Tiefpunkt T(-4.5|-5.15) |
| -4 | -5.0397 | 0.42 | 0.7 | -0.44 | |
| -3.5 | -4.7502 | 0.72 | 0.53 | -0.26 | |
| -3 | -4.3267 | 0.96 | 0.43 | -0.17 | |
| -2.5 | -3.7957 | 1.16 | 0.36 | -0.12 | |
| -2 | -3.1748 | 1.32 | 0.31 | -0.08 | |
| -1.5 | -2.4764 | 1.47 | 0.27 | -0.06 | |
| -1 | -1.71 | 1.6 | 0.24 | -0.05 | |
| -0.5 | -0.8826 | 1.71 | 0.22 | -0.04 | |
| 0 | 0 | 1.82 | 0.2 | -0.03 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.5 | 0.9331 | 1.91 | 0.19 | -0.03 | |
| 1 | 1.9129 | 2 | 0.17 | -0.02 | |
| 1.5 | 2.9362 | 2.09 | 0.16 | -0.02 | |
| 2 | 4 | 2.17 | 0.15 | -0.02 | |
| 2.5 | 5.1021 | 2.24 | 0.14 | -0.02 | |
| 3 | 6.2403 | 2.31 | 0.14 | -0.01 | |
| 3.5 | 7.4127 | 2.38 | 0.13 | -0.01 | |
| 4 | 8.6177 | 2.44 | 0.12 | -0.01 | |
| 4.5 | 9.8539 | 2.5 | 0.12 | -0.01 | |
| 5 | 11.1199 | 2.56 | 0.11 | -0.01 | |
| 5.5 | 12.4145 | 2.62 | 0.11 | -0.01 | |
| 6 | 13.7366 | 2.67 | 0.11 | -0.01 | |
| 6.5 | 15.0852 | 2.72 | 0.1 | -0.01 | |
| 7 | 16.4593 | 2.77 | 0.1 | -0.01 | |
| 7.5 | 17.8583 | 2.82 | 0.1 | -0.01 | |
| 8 | 19.2811 | 2.87 | 0.09 | -0.01 | |
| 8.5 | 20.7272 | 2.91 | 0.09 | -0.01 | |
| 9 | 22.1959 | 2.96 | 0.09 | 0 | |
| 9.5 | 23.6865 | 3 | 0.09 | 0 | |
| 10 | 25.1984 | 3.04 | 0.08 | 0 | |
| 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