www.michael-buhlmann.de
Funktion: f(x) = 2·ln(x+1)-3·ln(x+3), Df = (-1; +∞), Wf = (-∞; -2.6027], 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 | -4.1352 | 2.8 | -7.52 | 31.52 | |
0 | -3.2958 | 1 | -1.67 | 3.77 | Schnittpunkt Sy(0|-3.3) |
0.5 | -2.9474 | 0.48 | -0.64 | 1.04 | |
1 | -2.7726 | 0.25 | -0.31 | 0.41 | |
1.5 | -2.6797 | 0.13 | -0.17 | 0.19 | |
2 | -2.6311 | 0.07 | -0.1 | 0.1 | |
2.5 | -2.6087 | 0.03 | -0.06 | 0.06 | |
3 | -2.6027 | 0 | -0.04 | 0.03 | Hochpunkt H(3|-2.6) |
3.5 | -2.6073 | -0.02 | -0.03 | 0.02 | |
4 | -2.6189 | -0.03 | -0.02 | 0.01 | |
4.5 | -2.6352 | -0.04 | -0.01 | 0.01 | |
5 | -2.6548 | -0.04 | -0.01 | 0.01 | |
5.5 | -2.6766 | -0.05 | -0.01 | 0 | |
6 | -2.6999 | -0.05 | 0 | 0 | |
6.5 | -2.7241 | -0.05 | 0 | 0 | |
7 | -2.7489 | -0.05 | 0 | 0 | |
7.5 | -2.774 | -0.05 | 0 | 0 | |
7.898 | -2.7941 | -0.05 | 0 | 0 | Wendepunkt W(7.9|-2.79) |
8 | -2.7992 | -0.05 | 0 | 0 | |
8.5 | -2.8245 | -0.05 | 0 | 0 | |
9 | -2.8495 | -0.05 | 0 | 0 | |
9.5 | -2.8744 | -0.05 | 0 | 0 | |
10 | -2.8991 | -0.05 | 0 | 0 | |
Graph: | |||||
![]() |
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