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Funktion: f(x) = , Df = R, Wf = [0; +∞), Kubikwurzelfunktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 4.6416 | -0.31 | -0.01 | 0 | |
-9.5 | 4.4856 | -0.31 | -0.01 | 0 | |
-9 | 4.3267 | -0.32 | -0.01 | 0 | |
-8.5 | 4.165 | -0.33 | -0.01 | 0 | |
-8 | 4 | -0.33 | -0.01 | 0 | |
-7.5 | 3.8315 | -0.34 | -0.02 | 0 | |
-7 | 3.6593 | -0.35 | -0.02 | 0 | |
-6.5 | 3.4829 | -0.36 | -0.02 | 0 | |
-6 | 3.3019 | -0.37 | -0.02 | 0 | |
-5.5 | 3.1158 | -0.38 | -0.02 | -0.01 | |
-5 | 2.924 | -0.39 | -0.03 | -0.01 | |
-4.5 | 2.7257 | -0.4 | -0.03 | -0.01 | |
-4 | 2.5198 | -0.42 | -0.03 | -0.01 | |
-3.5 | 2.3052 | -0.44 | -0.04 | -0.02 | |
-3 | 2.0801 | -0.46 | -0.05 | -0.02 | |
-2.5 | 1.842 | -0.49 | -0.07 | -0.04 | |
-2 | 1.5874 | -0.53 | -0.09 | -0.06 | |
-1.5 | 1.3104 | -0.58 | -0.13 | -0.12 | |
-1 | 1 | -0.67 | -0.22 | -0.3 | |
-0.5 | 0.63 | -0.84 | -0.56 | -1.53 | |
0 | 0 | Infinity | Infinity | Infinity | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
0.5 | 0.63 | 0.84 | -0.56 | 1.46 | |
1 | 1 | 0.67 | -0.22 | 0.29 | |
1.5 | 1.3104 | 0.58 | -0.13 | 0.11 | |
2 | 1.5874 | 0.53 | -0.09 | 0.06 | |
2.5 | 1.842 | 0.49 | -0.07 | 0.03 | |
3 | 2.0801 | 0.46 | -0.05 | 0.02 | |
3.5 | 2.3052 | 0.44 | -0.04 | 0.02 | |
4 | 2.5198 | 0.42 | -0.03 | 0.01 | |
4.5 | 2.7257 | 0.4 | -0.03 | 0.01 | |
5 | 2.924 | 0.39 | -0.03 | 0.01 | |
5.5 | 3.1158 | 0.38 | -0.02 | 0.01 | |
6 | 3.3019 | 0.37 | -0.02 | 0 | |
6.5 | 3.4829 | 0.36 | -0.02 | 0 | |
7 | 3.6593 | 0.35 | -0.02 | 0 | |
7.5 | 3.8315 | 0.34 | -0.02 | 0 | |
8 | 4 | 0.33 | -0.01 | 0 | |
8.5 | 4.165 | 0.33 | -0.01 | 0 | |
9 | 4.3267 | 0.32 | -0.01 | 0 | |
9.5 | 4.4856 | 0.31 | -0.01 | 0 | |
10 | 4.6416 | 0.31 | -0.01 | 0 | |
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