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Funktion: f(x) = 4/x2-6·ln(x2), 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 | -9.1703 | 0.41 | 0.04 | 0.01 | |
| -9.5 | -8.9608 | 0.43 | 0.05 | 0.01 | |
| -9 | -8.7395 | 0.46 | 0.05 | 0.01 | |
| -8.5 | -8.5049 | 0.48 | 0.06 | 0.02 | |
| -8 | -8.2553 | 0.52 | 0.07 | 0.02 | |
| -7.5 | -7.9885 | 0.55 | 0.08 | 0.02 | |
| -7 | -7.702 | 0.59 | 0.09 | 0.03 | |
| -6.5 | -7.3925 | 0.64 | 0.11 | 0.04 | |
| -6 | -7.0559 | 0.7 | 0.13 | 0.05 | |
| -5.5 | -6.6868 | 0.78 | 0.16 | 0.07 | |
| -5 | -6.2778 | 0.86 | 0.2 | 0.09 | |
| -4.5 | -5.8188 | 0.98 | 0.26 | 0.14 | |
| -4 | -5.2952 | 1.13 | 0.34 | 0.22 | |
| -3.5 | -4.6845 | 1.33 | 0.49 | 0.37 | |
| -3 | -3.95 | 1.63 | 0.74 | 0.69 | |
| -2.5 | -3.0252 | 2.11 | 1.25 | 1.5 | |
| -2 | -1.7726 | 3 | 2.5 | 4.01 | |
| -1.532 | 0 | 4.84 | 6.06 | 13.64 | Nullstelle N(-1.53|0) |
| -1.5 | 0.1559 | 5.04 | 6.52 | 15.06 | |
| -1 | 4 | 12 | 28 | 104.51 | |
| -0.5 | 18.7726 | 72 | 400.01 | 3167.48 | |
| 0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> +∞, x -> 0+: f(x) -> +∞ |
| 0.5 | 18.7726 | -72 | 400.01 | -3105.26 | |
| 1 | 4 | -12 | 28 | -103.5 | |
| 1.5 | 0.1559 | -5.04 | 6.52 | -14.97 | |
| 1.53 | 0 | -4.85 | 6.09 | -13.64 | Nullstelle N(1.53|0) |
| 2 | -1.7726 | -3 | 2.5 | -3.99 | |
| 2.5 | -3.0252 | -2.11 | 1.25 | -1.49 | |
| 3 | -3.95 | -1.63 | 0.74 | -0.69 | |
| 3.5 | -4.6845 | -1.33 | 0.49 | -0.37 | |
| 4 | -5.2952 | -1.13 | 0.34 | -0.22 | |
| 4.5 | -5.8188 | -0.98 | 0.26 | -0.14 | |
| 5 | -6.2778 | -0.86 | 0.2 | -0.09 | |
| 5.5 | -6.6868 | -0.78 | 0.16 | -0.07 | |
| 6 | -7.0559 | -0.7 | 0.13 | -0.05 | |
| 6.5 | -7.3925 | -0.64 | 0.11 | -0.04 | |
| 7 | -7.702 | -0.59 | 0.09 | -0.03 | |
| 7.5 | -7.9885 | -0.55 | 0.08 | -0.02 | |
| 8 | -8.2553 | -0.52 | 0.07 | -0.02 | |
| 8.5 | -8.5049 | -0.48 | 0.06 | -0.02 | |
| 9 | -8.7395 | -0.46 | 0.05 | -0.01 | |
| 9.5 | -8.9608 | -0.43 | 0.05 | -0.01 | |
| 10 | -9.1703 | -0.41 | 0.04 | -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