, Df = R\{0; 4}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> 0 = y als Grenzkurve, x -> +∞: f(x) -> 0 = y als Grenzkurve ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R\{0; 4}, Wf = R, gebrochen rationale 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 | -0.4429 | -0.04 | -0.01 | 0 | |
| -9.5 | -0.4639 | -0.04 | -0.01 | 0 | |
| -9 | -0.4872 | -0.05 | -0.01 | 0 | |
| -8.5 | -0.5129 | -0.05 | -0.01 | 0 | |
| -8 | -0.5417 | -0.06 | -0.01 | 0 | |
| -7.5 | -0.5739 | -0.07 | -0.02 | -0.01 | |
| -7 | -0.6104 | -0.08 | -0.02 | -0.01 | |
| -6.5 | -0.652 | -0.09 | -0.03 | -0.01 | |
| -6 | -0.7 | -0.1 | -0.03 | -0.02 | |
| -5.5 | -0.756 | -0.12 | -0.04 | -0.02 | |
| -5 | -0.8222 | -0.14 | -0.05 | -0.03 | |
| -4.5 | -0.902 | -0.18 | -0.07 | -0.05 | |
| -4 | -1 | -0.22 | -0.1 | -0.07 | |
| -3.5 | -1.1238 | -0.28 | -0.15 | -0.12 | |
| -3 | -1.2857 | -0.37 | -0.23 | -0.23 | |
| -2.5 | -1.5077 | -0.53 | -0.4 | -0.47 | |
| -2 | -1.8333 | -0.81 | -0.77 | -1.14 | |
| -1.5 | -2.3636 | -1.4 | -1.8 | -3.57 | |
| -1 | -3.4 | -3.08 | -6.03 | -18.06 | |
| -0.5 | -6.4444 | -12.1 | -48.04 | -289.19 | |
| 0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 mit Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> +∞ |
| 0.5 | 5.4286 | -12.16 | 47.91 | -286.93 | |
| 1 | 2.3333 | -3.22 | 5.85 | -18.11 | |
| 1.5 | 1.2 | -1.65 | 1.52 | -3.86 | |
| 2 | 0.5 | -1.25 | 0.25 | -1.87 | |
| 2.134 | 0.334 | -1.23 | 0 | -1.86 | Wendepunkt W(2.13|0.33) |
| 2.4 | 0 | -1.3 | -0.54 | -2.38 | Nullstelle N(2.4|0) |
| 2.5 | -0.1333 | -1.37 | -0.8 | -2.83 | |
| 3 | -1 | -2.33 | -3.78 | -12.25 | |
| 3.5 | -3.1429 | -8.24 | -31.86 | -192.89 | |
| 4 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 4 mit Vorzeichenwechsel: x -> 4-: f(x) -> -∞, x -> 4+: f(x) -> +∞ |
| 4.5 | 4.6667 | -8.15 | 32.07 | -191.28 | |
| 5 | 2.6 | -2.12 | 4.05 | -12 | |
| 5.5 | 1.8788 | -0.99 | 1.22 | -2.39 | |
| 6 | 1.5 | -0.58 | 0.53 | -0.76 | |
| 6.5 | 1.2615 | -0.39 | 0.28 | -0.32 | |
| 7 | 1.0952 | -0.28 | 0.17 | -0.16 | |
| 7.5 | 0.9714 | -0.22 | 0.11 | -0.09 | |
| 8 | 0.875 | -0.17 | 0.07 | -0.05 | |
| 8.5 | 0.7974 | -0.14 | 0.05 | -0.03 | |
| 9 | 0.7333 | -0.12 | 0.04 | -0.02 | |
| 9.5 | 0.6794 | -0.1 | 0.03 | -0.02 | |
| 10 | 0.6333 | -0.09 | 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