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Funktion: f(x) = , Df = R\{0}, Wf = R\(-1.4344; 1.4344), Wurzelfunktion, Funktion punktsymmetrisch zu O(0|0), x -> -∞: f(x) -> 3√x = y als Grenzkurve, x -> +∞: f(x) -> 3√x = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | -2.7145 | 0.05 | 0 | 0 | |
-19.5 | -2.6917 | 0.05 | 0 | 0 | |
-19 | -2.6685 | 0.05 | 0 | 0 | |
-18.5 | -2.6448 | 0.05 | 0 | 0 | |
-18 | -2.6208 | 0.05 | 0 | 0 | |
-17.5 | -2.5963 | 0.05 | 0 | 0 | |
-17 | -2.5714 | 0.05 | 0 | 0 | |
-16.5 | -2.5459 | 0.05 | 0 | 0 | |
-16 | -2.5199 | 0.05 | 0 | 0 | |
-15.5 | -2.4934 | 0.05 | 0 | 0 | |
-15 | -2.4663 | 0.05 | 0 | 0 | |
-14.5 | -2.4386 | 0.06 | 0 | 0 | |
-14 | -2.4103 | 0.06 | 0 | 0 | |
-13.5 | -2.3813 | 0.06 | 0 | 0 | |
-13 | -2.3516 | 0.06 | 0 | 0 | |
-12.5 | -2.321 | 0.06 | 0 | 0 | |
-12 | -2.2897 | 0.06 | 0 | 0 | |
-11.5 | -2.2575 | 0.07 | 0 | 0 | |
-11 | -2.2244 | 0.07 | 0 | 0 | |
-10.5 | -2.1902 | 0.07 | 0 | 0 | |
-10 | -2.155 | 0.07 | 0 | 0 | |
-9.5 | -2.1186 | 0.07 | 0.01 | 0 | |
-9 | -2.0809 | 0.08 | 0.01 | 0 | |
-8.5 | -2.0419 | 0.08 | 0.01 | 0 | |
-8 | -2.0013 | 0.08 | 0.01 | 0 | |
-7.5 | -1.9591 | 0.09 | 0.01 | 0 | |
-7 | -1.9151 | 0.09 | 0.01 | 0 | |
-6.5 | -1.869 | 0.09 | 0.01 | 0 | |
-6 | -1.8209 | 0.1 | 0.01 | 0 | |
-5.5 | -1.7703 | 0.1 | 0.01 | 0 | |
-5 | -1.7172 | 0.11 | 0.01 | 0 | |
-4.5 | -1.6616 | 0.11 | 0.01 | 0 | |
-4 | -1.6038 | 0.12 | 0.01 | -0.01 | |
-3.738 | -1.5729 | 0.12 | 0 | -0.03 | Wendepunkt W(-3.74|-1.57) |
-3.5 | -1.5448 | 0.12 | -0.01 | -0.04 | |
-3 | -1.4882 | 0.11 | -0.04 | -0.12 | |
-2.5 | -1.4442 | 0.06 | -0.15 | -0.35 | |
-2.214 | -1.4344 | 0 | -0.29 | -0.66 | Hochpunkt H(-2.21|-1.43) |
-2 | -1.4422 | -0.08 | -0.47 | -1.05 | |
-1.5 | -1.5701 | -0.51 | -1.38 | -2.93 | |
-1 | -2.0801 | -1.77 | -4.38 | -12.08 | |
-0.5 | -4.0104 | -7.94 | -32.25 | -193.1 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 mit Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> +∞ |
0.5 | 4.0104 | -7.94 | 32.25 | -190.02 | |
1 | 2.0801 | -1.77 | 4.38 | -11.99 | |
1.5 | 1.5701 | -0.51 | 1.38 | -2.91 | |
2 | 1.4422 | -0.08 | 0.47 | -1.04 | |
2.212 | 1.4344 | 0 | 0.29 | -0.66 | Tiefpunkt T(2.21|1.43) |
2.5 | 1.4442 | 0.06 | 0.15 | -0.35 | |
3 | 1.4882 | 0.11 | 0.04 | -0.12 | |
3.5 | 1.5448 | 0.12 | 0.01 | -0.04 | |
3.736 | 1.5726 | 0.12 | 0 | -0.03 | Wendepunkt W(3.74|1.57) |
4 | 1.6038 | 0.12 | -0.01 | -0.01 | |
4.5 | 1.6616 | 0.11 | -0.01 | 0 | |
5 | 1.7172 | 0.11 | -0.01 | 0 | |
5.5 | 1.7703 | 0.1 | -0.01 | 0 | |
6 | 1.8209 | 0.1 | -0.01 | 0 | |
6.5 | 1.869 | 0.09 | -0.01 | 0 | |
7 | 1.9151 | 0.09 | -0.01 | 0 | |
7.5 | 1.9591 | 0.09 | -0.01 | 0 | |
8 | 2.0013 | 0.08 | -0.01 | 0 | |
8.5 | 2.0419 | 0.08 | -0.01 | 0 | |
9 | 2.0809 | 0.08 | -0.01 | 0 | |
9.5 | 2.1186 | 0.07 | -0.01 | 0 | |
10 | 2.155 | 0.07 | 0 | 0 | |
10.5 | 2.1902 | 0.07 | 0 | 0 | |
11 | 2.2244 | 0.07 | 0 | 0 | |
11.5 | 2.2575 | 0.07 | 0 | 0 | |
12 | 2.2897 | 0.06 | 0 | 0 | |
12.5 | 2.321 | 0.06 | 0 | 0 | |
13 | 2.3516 | 0.06 | 0 | 0 | |
13.5 | 2.3813 | 0.06 | 0 | 0 | |
14 | 2.4103 | 0.06 | 0 | 0 | |
14.5 | 2.4386 | 0.06 | 0 | 0 | |
15 | 2.4663 | 0.05 | 0 | 0 | |
15.5 | 2.4934 | 0.05 | 0 | 0 | |
16 | 2.5199 | 0.05 | 0 | 0 | |
16.5 | 2.5459 | 0.05 | 0 | 0 | |
17 | 2.5714 | 0.05 | 0 | 0 | |
17.5 | 2.5963 | 0.05 | 0 | 0 | |
18 | 2.6208 | 0.05 | 0 | 0 | |
18.5 | 2.6448 | 0.05 | 0 | 0 | |
19 | 2.6685 | 0.05 | 0 | 0 | |
19.5 | 2.6917 | 0.05 | 0 | 0 | |
20 | 2.7145 | 0.05 | 0 | 0 | |
Graph: | |||||
Graph(en) der Asymptote(n), Grenzkurve(n).
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