, Df = R\{0}, Wf = (-∞; 0.6863], reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> 0 = y als Grenzkurve ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R\{0}, Wf = (-∞; 0.6863], reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> 0 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -63.8177 | 25.08 | -10.58 | 4.57 | |
| -9.5 | -52.5092 | 20.32 | -8.53 | 3.66 | |
| -9 | -43.3416 | 16.48 | -6.88 | 2.93 | |
| -8.5 | -35.9017 | 13.38 | -5.56 | 2.35 | |
| -8 | -29.8584 | 10.88 | -4.51 | 1.89 | |
| -7.5 | -24.9457 | 8.84 | -3.66 | 1.51 | |
| -7 | -20.9506 | 7.19 | -2.98 | 1.21 | |
| -6.5 | -17.7022 | 5.85 | -2.43 | 0.97 | |
| -6 | -15.0642 | 4.74 | -2 | 0.77 | |
| -5.5 | -12.9278 | 3.83 | -1.66 | 0.6 | |
| -5 | -11.2079 | 3.07 | -1.4 | 0.45 | |
| -4.5 | -9.8391 | 2.42 | -1.21 | 0.3 | |
| -4 | -8.7745 | 1.85 | -1.1 | 0.14 | |
| -3.5 | -7.986 | 1.31 | -1.08 | -0.08 | |
| -3 | -7.4695 | 0.75 | -1.2 | -0.48 | |
| -2.5 | -7.2599 | 0.06 | -1.64 | -1.41 | |
| -2.47 | -7.259 | 0 | -1.68 | -1.5 | Hochpunkt H(-2.47|-7.26) |
| -2 | -7.4753 | -1.02 | -2.89 | -4.21 | |
| -1.5 | -8.468 | -3.29 | -7.14 | -16.13 | |
| -1 | -11.541 | -10.72 | -29.27 | -107.43 | |
| -0.5 | -25.6805 | -69.38 | -376.45 | -2976.59 | |
| 0 | Infinity | Infinity | Infinity | Infinity | senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> -∞ |
| 0.5 | -3.1152 | 26.51 | -200.31 | 1687.56 | |
| 0.75 | 0 | 4.89 | -30.97 | 192.13 | Nullstelle N(0.75|0) |
| 1 | 0.6065 | 0.91 | -7.13 | 37.94 | |
| 1.21 | 0.6863 | 0 | -2.31 | 12.1 | Hochpunkt H(1.21|0.69) |
| 1.5 | 0.6298 | -0.31 | -0.4 | 2.93 | |
| 1.71 | 0.5585 | -0.35 | 0 | 1.07 | Wendepunkt W(1.71|0.56) |
| 2 | 0.4598 | -0.32 | 0.16 | 0.21 | |
| 2.5 | 0.3209 | -0.23 | 0.17 | -0.08 | |
| 3 | 0.2231 | -0.16 | 0.12 | -0.09 | |
| 3.5 | 0.156 | -0.11 | 0.08 | -0.06 | |
| 4 | 0.11 | -0.08 | 0.06 | -0.04 | |
| 4.5 | 0.0781 | -0.05 | 0.04 | -0.03 | |
| 5 | 0.0558 | -0.04 | 0.03 | -0.02 | |
| 5.5 | 0.0402 | -0.03 | 0.02 | -0.01 | |
| 6 | 0.029 | -0.02 | 0.01 | -0.01 | |
| 6.5 | 0.0211 | -0.01 | 0.01 | -0.01 | |
| 7 | 0.0154 | -0.01 | 0.01 | 0 | |
| 7.5 | 0.0113 | -0.01 | 0 | 0 | |
| 8 | 0.0083 | -0.01 | 0 | 0 | |
| 8.5 | 0.0061 | 0 | 0 | 0 | |
| 9 | 0.0045 | 0 | 0 | 0 | |
| 9.5 | 0.0034 | 0 | 0 | 0 | |
| 10 | 0.0025 | 0 | 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