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Funktion: f(x) = , Df = R\[-4; 2], Wf = R\{0}, reelle Funktion, x -> -∞: f(x) -> 0 = y als Grenzkurve, x -> +∞: f(x) -> 0 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -0.6931 | -0.08 | -0.02 | -0.01 | |
-9.5 | -0.7376 | -0.09 | -0.03 | -0.01 | |
-9 | -0.7885 | -0.11 | -0.03 | -0.01 | |
-8.5 | -0.8473 | -0.13 | -0.04 | -0.02 | |
-8 | -0.9163 | -0.15 | -0.05 | -0.03 | |
-7.5 | -0.9985 | -0.18 | -0.07 | -0.04 | |
-7 | -1.0986 | -0.22 | -0.1 | -0.07 | |
-6.5 | -1.2238 | -0.28 | -0.15 | -0.12 | |
-6 | -1.3863 | -0.38 | -0.23 | -0.25 | |
-5.5 | -1.6094 | -0.53 | -0.43 | -0.59 | |
-5 | -1.9459 | -0.86 | -0.98 | -2 | |
-4.5 | -2.5649 | -1.85 | -3.98 | -16.04 | |
-4 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -4 |
2 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 2 |
2.5 | 2.5649 | -1.85 | 3.98 | -15.94 | |
3 | 1.9459 | -0.86 | 0.98 | -1.99 | |
3.5 | 1.6094 | -0.53 | 0.43 | -0.59 | |
4 | 1.3863 | -0.38 | 0.23 | -0.25 | |
4.5 | 1.2238 | -0.28 | 0.15 | -0.12 | |
5 | 1.0986 | -0.22 | 0.1 | -0.07 | |
5.5 | 0.9985 | -0.18 | 0.07 | -0.04 | |
6 | 0.9163 | -0.15 | 0.05 | -0.03 | |
6.5 | 0.8473 | -0.13 | 0.04 | -0.02 | |
7 | 0.7885 | -0.11 | 0.03 | -0.01 | |
7.5 | 0.7376 | -0.09 | 0.03 | -0.01 | |
8 | 0.6931 | -0.08 | 0.02 | -0.01 | |
8.5 | 0.6539 | -0.07 | 0.02 | -0.01 | |
9 | 0.619 | -0.07 | 0.01 | 0 | |
9.5 | 0.5878 | -0.06 | 0.01 | 0 | |
10 | 0.5596 | -0.05 | 0.01 | 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