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Funktion: f(x) = ln2(x), Df = (0; +∞), Wf = [0; +∞), 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 | 0.4805 | -2.77 | 13.55 | -69.94 | |
1 | 0 | 0 | 2 | -5.99 | Nullstelle N(1|0) = Tiefpunkt T(1|0) |
1.5 | 0.1644 | 0.54 | 0.53 | -1.3 | |
2 | 0.4805 | 0.69 | 0.15 | -0.4 | |
2.5 | 0.8396 | 0.73 | 0.03 | -0.15 | |
2.718 | 1 | 0.74 | 0 | -0.1 | Wendepunkt W(2.72|1) |
3 | 1.2069 | 0.73 | -0.02 | -0.06 | |
3.5 | 1.5694 | 0.72 | -0.04 | -0.02 | |
4 | 1.9218 | 0.69 | -0.05 | -0.01 | |
4.5 | 2.2622 | 0.67 | -0.05 | 0 | |
5 | 2.5903 | 0.64 | -0.05 | 0 | |
5.5 | 2.9062 | 0.62 | -0.05 | 0 | |
6 | 3.2104 | 0.6 | -0.04 | 0.01 | |
6.5 | 3.5036 | 0.58 | -0.04 | 0.01 | |
7 | 3.7866 | 0.56 | -0.04 | 0.01 | |
7.5 | 4.0598 | 0.54 | -0.04 | 0 | |
8 | 4.3241 | 0.52 | -0.03 | 0 | |
8.5 | 4.5799 | 0.5 | -0.03 | 0 | |
9 | 4.8278 | 0.49 | -0.03 | 0 | |
9.5 | 5.0683 | 0.47 | -0.03 | 0 | |
10 | 5.3019 | 0.46 | -0.03 | 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, 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