www.michael-buhlmann.de
Funktion: f(x) = 3√x, Df = R, Wf = R, Kubikwurzelfunktion, Funktion punktsymmetrisch zum Punkt O(0|0), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -2.1544 | 0.07 | 0 | 0 | |
-9.5 | -2.1179 | 0.07 | 0.01 | 0 | |
-9 | -2.0801 | 0.08 | 0.01 | 0 | |
-8.5 | -2.0408 | 0.08 | 0.01 | 0 | |
-8 | -2 | 0.08 | 0.01 | 0 | |
-7.5 | -1.9574 | 0.09 | 0.01 | 0 | |
-7 | -1.9129 | 0.09 | 0.01 | 0 | |
-6.5 | -1.8663 | 0.1 | 0.01 | 0 | |
-6 | -1.8171 | 0.1 | 0.01 | 0 | |
-5.5 | -1.7652 | 0.11 | 0.01 | 0 | |
-5 | -1.71 | 0.11 | 0.02 | 0.01 | |
-4.5 | -1.651 | 0.12 | 0.02 | 0.01 | |
-4 | -1.5874 | 0.13 | 0.02 | 0.01 | |
-3.5 | -1.5183 | 0.14 | 0.03 | 0.01 | |
-3 | -1.4422 | 0.16 | 0.04 | 0.02 | |
-2.5 | -1.3572 | 0.18 | 0.05 | 0.03 | |
-2 | -1.2599 | 0.21 | 0.07 | 0.06 | |
-1.5 | -1.1447 | 0.25 | 0.11 | 0.13 | |
-1 | -1 | 0.33 | 0.22 | 0.38 | |
-0.5 | -0.7937 | 0.53 | 0.71 | 2.42 | |
0 | 0 | Infinity | Infinity | Infinity | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
0.5 | 0.7937 | 0.53 | -0.71 | 2.29 | |
1 | 1 | 0.33 | -0.22 | 0.37 | |
1.5 | 1.1447 | 0.25 | -0.11 | 0.12 | |
2 | 1.2599 | 0.21 | -0.07 | 0.06 | |
2.5 | 1.3572 | 0.18 | -0.05 | 0.03 | |
3 | 1.4422 | 0.16 | -0.04 | 0.02 | |
3.5 | 1.5183 | 0.14 | -0.03 | 0.01 | |
4 | 1.5874 | 0.13 | -0.02 | 0.01 | |
4.5 | 1.651 | 0.12 | -0.02 | 0.01 | |
5 | 1.71 | 0.11 | -0.02 | 0.01 | |
5.5 | 1.7652 | 0.11 | -0.01 | 0 | |
6 | 1.8171 | 0.1 | -0.01 | 0 | |
6.5 | 1.8663 | 0.1 | -0.01 | 0 | |
7 | 1.9129 | 0.09 | -0.01 | 0 | |
7.5 | 1.9574 | 0.09 | -0.01 | 0 | |
8 | 2 | 0.08 | -0.01 | 0 | |
8.5 | 2.0408 | 0.08 | -0.01 | 0 | |
9 | 2.0801 | 0.08 | -0.01 | 0 | |
9.5 | 2.1179 | 0.07 | -0.01 | 0 | |
10 | 2.1544 | 0.07 | 0 | 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