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Funktion: f(x) = , Df = R\{0}, Wf = R, Wurzelfunktion, 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 | -1.572 | 0.03 | 0 | 0 | |
-9.5 | -1.5546 | 0.04 | 0 | 0 | |
-9 | -1.5362 | 0.04 | 0 | 0 | |
-8.5 | -1.5168 | 0.04 | 0 | 0 | |
-8 | -1.4963 | 0.04 | 0.01 | 0 | |
-7.5 | -1.4744 | 0.05 | 0.01 | 0 | |
-7 | -1.4509 | 0.05 | 0.01 | 0 | |
-6.5 | -1.4254 | 0.05 | 0.01 | 0 | |
-6 | -1.3977 | 0.06 | 0.01 | 0.01 | |
-5.5 | -1.367 | 0.06 | 0.02 | 0.01 | |
-5 | -1.3324 | 0.07 | 0.02 | 0.01 | |
-4.5 | -1.2928 | 0.09 | 0.03 | 0.02 | |
-4 | -1.2457 | 0.1 | 0.04 | 0.04 | |
-3.5 | -1.1871 | 0.13 | 0.08 | 0.1 | |
-3 | -1.1076 | 0.19 | 0.17 | 0.33 | |
-2.5 | -0.9791 | 0.36 | 0.63 | 2.33 | |
-2 | 0 | Infinity | Infinity | Infinity | Nullstelle N(-2|0) = Wendepunkt W(-2|0) |
-1.5 | 1.0313 | 0.49 | -0.52 | 2.45 | |
-1.117 | 1.1976 | 0.41 | 0 | 0.93 | Wendepunkt W(-1.12|1.2) |
-1 | 1.2457 | 0.42 | 0.11 | 1 | |
-0.5 | 1.4963 | 0.68 | 1.32 | 6.47 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 mit Vorzeichenwechsel: x -> 0-: f(x) -> +∞, x -> 0+: f(x) -> -∞ |
0.5 | -1.4963 | 0.68 | -1.32 | 6.43 | |
1 | -1.2457 | 0.42 | -0.11 | 1 | |
1.116 | -1.1981 | 0.41 | 0 | 0.93 | Wendepunkt W(1.12|-1.2) |
1.5 | -1.0313 | 0.49 | 0.52 | 2.46 | |
2 | 0 | Infinity | Infinity | Infinity | Nullstelle N(2|0) = Wendepunkt W(2|0) |
2.5 | 0.9791 | 0.36 | -0.63 | 2.32 | |
3 | 1.1076 | 0.19 | -0.17 | 0.33 | |
3.5 | 1.1871 | 0.13 | -0.08 | 0.1 | |
4 | 1.2457 | 0.1 | -0.04 | 0.04 | |
4.5 | 1.2928 | 0.09 | -0.03 | 0.02 | |
5 | 1.3324 | 0.07 | -0.02 | 0.01 | |
5.5 | 1.367 | 0.06 | -0.02 | 0.01 | |
6 | 1.3977 | 0.06 | -0.01 | 0.01 | |
6.5 | 1.4254 | 0.05 | -0.01 | 0 | |
7 | 1.4509 | 0.05 | -0.01 | 0 | |
7.5 | 1.4744 | 0.05 | -0.01 | 0 | |
8 | 1.4963 | 0.04 | -0.01 | 0 | |
8.5 | 1.5168 | 0.04 | 0 | 0 | |
9 | 1.5362 | 0.04 | 0 | 0 | |
9.5 | 1.5546 | 0.04 | 0 | 0 | |
10 | 1.572 | 0.03 | 0 | 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, 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