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Funktion: f(x) = 5·ln(x)-3, 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 | -6.4657 | 10 | -20 | 77.69 | |
1 | -3 | 5 | -5 | 9.85 | |
1.5 | -0.9727 | 3.33 | -2.22 | 2.93 | |
1.82 | 0 | 2.75 | -1.51 | 1.65 | Nullstelle N(1.82|0) |
2 | 0.4657 | 2.5 | -1.25 | 1.24 | |
2.5 | 1.5815 | 2 | -0.8 | 0.64 | |
3 | 2.4931 | 1.67 | -0.56 | 0.37 | |
3.5 | 3.2638 | 1.43 | -0.41 | 0.23 | |
4 | 3.9315 | 1.25 | -0.31 | 0.16 | |
4.5 | 4.5204 | 1.11 | -0.25 | 0.11 | |
5 | 5.0472 | 1 | -0.2 | 0.08 | |
5.5 | 5.5237 | 0.91 | -0.17 | 0.06 | |
6 | 5.9588 | 0.83 | -0.14 | 0.05 | |
6.5 | 6.359 | 0.77 | -0.12 | 0.04 | |
7 | 6.7296 | 0.71 | -0.1 | 0.03 | |
7.5 | 7.0745 | 0.67 | -0.09 | 0.02 | |
8 | 7.3972 | 0.63 | -0.08 | 0.02 | |
8.5 | 7.7003 | 0.59 | -0.07 | 0.02 | |
9 | 7.9861 | 0.56 | -0.06 | 0.01 | |
9.5 | 8.2565 | 0.53 | -0.06 | 0.01 | |
10 | 8.5129 | 0.5 | -0.05 | 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