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Funktion: f(x) = , Df = (0; +∞), Wf = R, reelle Funktion, x -> 0: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 |
0.5 | -3.9693 | 6.27 | -12.12 | 47.38 | |
1 | -1.7678 | 3.22 | -3.08 | 6.01 | |
1.5 | -0.4503 | 2.19 | -1.4 | 1.8 | |
1.72 | 0 | 1.92 | -1.07 | 1.2 | Nullstelle N(1.72|0) |
2 | 0.4983 | 1.66 | -0.8 | 0.77 | |
2.5 | 1.2413 | 1.34 | -0.52 | 0.4 | |
3 | 1.8525 | 1.12 | -0.36 | 0.23 | |
3.5 | 2.3715 | 0.96 | -0.27 | 0.15 | |
4 | 2.8226 | 0.85 | -0.21 | 0.1 | |
4.5 | 3.2212 | 0.75 | -0.17 | 0.07 | |
5 | 3.5783 | 0.68 | -0.13 | 0.05 | |
5.5 | 3.9016 | 0.62 | -0.11 | 0.04 | |
6 | 4.1968 | 0.57 | -0.09 | 0.03 | |
6.5 | 4.4683 | 0.52 | -0.08 | 0.02 | |
7 | 4.7197 | 0.48 | -0.07 | 0.02 | |
7.5 | 4.9536 | 0.45 | -0.06 | 0.02 | |
8 | 5.1723 | 0.42 | -0.05 | 0.01 | |
8.5 | 5.3776 | 0.4 | -0.05 | 0.01 | |
9 | 5.5711 | 0.38 | -0.04 | 0.01 | |
9.5 | 5.7539 | 0.36 | -0.04 | 0.01 | |
10 | 5.9272 | 0.34 | -0.03 | 0.01 | |
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