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Funktion: f(x) = 0.5·ln(x4)+0.25·x2-1, Df = R\{0}, Wf = R, reelle Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 28.6052 | -5.2 | 0.48 | 0 | |
-9.5 | 26.0651 | -4.96 | 0.48 | 0 | |
-9 | 23.6444 | -4.72 | 0.48 | -0.01 | |
-8.5 | 21.3426 | -4.49 | 0.47 | -0.01 | |
-8 | 19.1589 | -4.25 | 0.47 | -0.01 | |
-7.5 | 17.0923 | -4.02 | 0.46 | -0.01 | |
-7 | 15.1418 | -3.79 | 0.46 | -0.01 | |
-6.5 | 13.3061 | -3.56 | 0.45 | -0.01 | |
-6 | 11.5835 | -3.33 | 0.44 | -0.02 | |
-5.5 | 9.972 | -3.11 | 0.43 | -0.02 | |
-5 | 8.4689 | -2.9 | 0.42 | -0.03 | |
-4.5 | 7.0707 | -2.69 | 0.4 | -0.04 | |
-4 | 5.7726 | -2.5 | 0.37 | -0.06 | |
-3.5 | 4.568 | -2.32 | 0.34 | -0.09 | |
-3 | 3.4472 | -2.17 | 0.28 | -0.15 | |
-2.5 | 2.3951 | -2.05 | 0.18 | -0.26 | |
-2.002 | 1.3903 | -2 | 0 | -0.5 | Wendepunkt W(-2|1.39) |
-2 | 1.3863 | -2 | 0 | -0.5 | |
-1.5 | 0.3734 | -2.08 | -0.39 | -1.19 | |
-1.326 | 0 | -2.17 | -0.64 | -1.72 | Nullstelle N(-1.33|0) |
-1 | -0.75 | -2.5 | -1.5 | -4.01 | |
-0.5 | -2.3238 | -4.25 | -7.5 | -32.19 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> -∞ |
0.5 | -2.3238 | 4.25 | -7.5 | 31.81 | |
1 | -0.75 | 2.5 | -1.5 | 3.99 | |
1.326 | 0 | 2.17 | -0.64 | 1.72 | Nullstelle N(1.33|0) |
1.5 | 0.3734 | 2.08 | -0.39 | 1.18 | |
2 | 1.3863 | 2 | 0 | 0.5 | Wendepunkt W(2|1.39) |
2.5 | 2.3951 | 2.05 | 0.18 | 0.26 | |
3 | 3.4472 | 2.17 | 0.28 | 0.15 | |
3.5 | 4.568 | 2.32 | 0.34 | 0.09 | |
4 | 5.7726 | 2.5 | 0.37 | 0.06 | |
4.5 | 7.0707 | 2.69 | 0.4 | 0.04 | |
5 | 8.4689 | 2.9 | 0.42 | 0.03 | |
5.5 | 9.972 | 3.11 | 0.43 | 0.02 | |
6 | 11.5835 | 3.33 | 0.44 | 0.02 | |
6.5 | 13.3061 | 3.56 | 0.45 | 0.01 | |
7 | 15.1418 | 3.79 | 0.46 | 0.01 | |
7.5 | 17.0923 | 4.02 | 0.46 | 0.01 | |
8 | 19.1589 | 4.25 | 0.47 | 0.01 | |
8.5 | 21.3426 | 4.49 | 0.47 | 0.01 | |
9 | 23.6444 | 4.72 | 0.48 | 0.01 | |
9.5 | 26.0651 | 4.96 | 0.48 | 0 | |
10 | 28.6052 | 5.2 | 0.48 | 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