, Df = R\{-3; 0}, Wf = R\{0}, 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\{-3; 0}, Wf = R\{0}, 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 | -0.2457 | -0.03 | -0.01 | 0 | |
| -9.5 | -0.2634 | -0.04 | -0.01 | -0.01 | |
| -9 | -0.284 | -0.04 | -0.01 | -0.01 | |
| -8.5 | -0.3083 | -0.05 | -0.02 | -0.01 | |
| -8 | -0.3375 | -0.06 | -0.03 | -0.02 | |
| -7.5 | -0.3733 | -0.08 | -0.04 | -0.03 | |
| -7 | -0.4184 | -0.1 | -0.05 | -0.04 | |
| -6.5 | -0.4768 | -0.13 | -0.08 | -0.07 | |
| -6 | -0.5556 | -0.19 | -0.13 | -0.14 | |
| -5.5 | -0.6678 | -0.27 | -0.23 | -0.29 | |
| -5 | -0.84 | -0.44 | -0.46 | -0.72 | |
| -4.5 | -1.1358 | -0.8 | -1.13 | -2.32 | |
| -4 | -1.75 | -1.88 | -3.91 | -11.93 | |
| -3.5 | -3.6735 | -7.81 | -31.84 | -192.59 | |
| -3 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -3 mit Vorzeichenwechsel: x -> -3-: f(x) -> -∞, x -> -3+: f(x) -> +∞ |
| -2.5 | 4.64 | -7.49 | 32.61 | -190.25 | |
| -2 | 3 | -1 | 5.5 | -8.97 | |
| -1.797 | 2.9012 | 0 | 4.6 | -0.59 | Tiefpunkt T(-1.8|2.9) |
| -1.5 | 3.1111 | 1.48 | 5.93 | 10.3 | |
| -1 | 5 | 7.5 | 24.5 | 95.49 | |
| -0.5 | 16.8 | 63.68 | 384.26 | 3087.15 | |
| 0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> +∞, x -> 0+: f(x) -> +∞ |
| 0.5 | 16.5714 | -64.16 | 384.1 | -3056.81 | |
| 1 | 4.5 | -8.13 | 24.06 | -95.81 | |
| 1.5 | 2.2222 | -2.47 | 4.78 | -12.65 | |
| 2 | 1.4 | -1.08 | 1.53 | -3.02 | |
| 2.5 | 1.0036 | -0.58 | 0.64 | -1 | |
| 3 | 0.7778 | -0.35 | 0.31 | -0.4 | |
| 3.5 | 0.6342 | -0.23 | 0.17 | -0.19 | |
| 4 | 0.5357 | -0.17 | 0.11 | -0.1 | |
| 4.5 | 0.4642 | -0.12 | 0.07 | -0.06 | |
| 5 | 0.41 | -0.1 | 0.05 | -0.03 | |
| 5.5 | 0.3675 | -0.08 | 0.03 | -0.02 | |
| 6 | 0.3333 | -0.06 | 0.02 | -0.01 | |
| 6.5 | 0.3052 | -0.05 | 0.02 | -0.01 | |
| 7 | 0.2816 | -0.04 | 0.01 | -0.01 | |
| 7.5 | 0.2616 | -0.04 | 0.01 | -0.01 | |
| 8 | 0.2443 | -0.03 | 0.01 | 0 | |
| 8.5 | 0.2293 | -0.03 | 0.01 | 0 | |
| 9 | 0.216 | -0.02 | 0.01 | 0 | |
| 9.5 | 0.2043 | -0.02 | 0 | 0 | |
| 10 | 0.1938 | -0.02 | 0 | 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