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Funktion: f(x) = ln3(x+3)-5·ln(x+1), Df = (-1; +∞), Wf = [-1.3346; +∞), reelle Funktion, x -> -1: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-1 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -1 |
-0.5 | 4.235 | -8.99 | 20.48 | -79.87 | |
0 | 1.326 | -3.79 | 5.33 | -10.21 | Schnittpunkt Sy(0|1.33) |
0.468 | 0 | -2.07 | 2.55 | -3.32 | Nullstelle N(0.47|0) |
0.5 | -0.0612 | -1.99 | 2.45 | -3.12 | |
1 | -0.8015 | -1.06 | 1.41 | -1.36 | |
1.5 | -1.1789 | -0.49 | 0.91 | -0.72 | |
2 | -1.3241 | -0.11 | 0.63 | -0.43 | |
2.188 | -1.3346 | 0 | 0.56 | -0.36 | Tiefpunkt T(2.19|-1.33) |
2.5 | -1.3095 | 0.16 | 0.46 | -0.28 | |
3 | -1.1792 | 0.36 | 0.34 | -0.19 | |
3.5 | -0.9623 | 0.51 | 0.26 | -0.13 | |
4 | -0.6789 | 0.62 | 0.21 | -0.1 | |
4.5 | -0.3436 | 0.71 | 0.16 | -0.07 | |
4.958 | 0 | 0.78 | 0.13 | -0.06 | Nullstelle N(4.96|0) |
5 | 0.0329 | 0.79 | 0.13 | -0.06 | |
5.5 | 0.4422 | 0.85 | 0.11 | -0.04 | |
6 | 0.8782 | 0.89 | 0.09 | -0.04 | |
6.5 | 1.3357 | 0.93 | 0.07 | -0.03 | |
7 | 1.8109 | 0.97 | 0.06 | -0.02 | |
7.5 | 2.3003 | 0.99 | 0.05 | -0.02 | |
8 | 2.8015 | 1.01 | 0.04 | -0.02 | |
8.5 | 3.3123 | 1.03 | 0.03 | -0.01 | |
9 | 3.8308 | 1.04 | 0.02 | -0.01 | |
9.5 | 4.3555 | 1.05 | 0.02 | -0.01 | |
10 | 4.8852 | 1.06 | 0.02 | -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