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Funktion: f(x) = 4·e-1/x, Df = R\{0}, Wf = (0; +∞)\{4}, reelle Funktion, x -> -∞: f(x) -> 4 = y als Grenzkurve, x -> +∞: f(x) -> 4 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 4.4207 | 0.04 | 0.01 | 0 | |
| -9.5 | 4.444 | 0.05 | 0.01 | 0 | |
| -9 | 4.4701 | 0.06 | 0.01 | 0 | |
| -8.5 | 4.4994 | 0.06 | 0.02 | 0.01 | |
| -8 | 4.5326 | 0.07 | 0.02 | 0.01 | |
| -7.5 | 4.5705 | 0.08 | 0.02 | 0.01 | |
| -7 | 4.6143 | 0.09 | 0.03 | 0.01 | |
| -6.5 | 4.6652 | 0.11 | 0.04 | 0.02 | |
| -6 | 4.7254 | 0.13 | 0.05 | 0.03 | |
| -5.5 | 4.7976 | 0.16 | 0.06 | 0.04 | |
| -5 | 4.8856 | 0.2 | 0.09 | 0.06 | |
| -4.5 | 4.9954 | 0.25 | 0.12 | 0.09 | |
| -4 | 5.1361 | 0.32 | 0.18 | 0.15 | |
| -3.5 | 5.3228 | 0.43 | 0.28 | 0.28 | |
| -3 | 5.5824 | 0.62 | 0.48 | 0.56 | |
| -2.5 | 5.9673 | 0.95 | 0.92 | 1.31 | |
| -2 | 6.5949 | 1.65 | 2.06 | 3.84 | |
| -1.5 | 7.7909 | 3.46 | 6.16 | 16.21 | |
| -1 | 10.8731 | 10.87 | 32.62 | 143.37 | |
| -0.5 | 29.5562 | 118.27 | 946.1 | 10778.53 | |
| 0 | 0 / Infinity | 0 / Infinity | 0 / Infinity | 0 / Infinity | Senkrechte Asymptote/Pol: x = 0 mit: x -> 0-: f(x) -> +∞ bzw. hebbare Lücke L(0|0) bei x > 0 |
| 0.5 | 0.5413 | 2.17 | 0 | -16.98 | Wendepunkt W(0.5|0.54) |
| 1 | 1.4715 | 1.47 | -1.47 | 1.48 | |
| 1.5 | 2.0537 | 0.91 | -0.81 | 0.99 | |
| 2 | 2.4261 | 0.61 | -0.45 | 0.49 | |
| 2.5 | 2.6813 | 0.43 | -0.27 | 0.26 | |
| 3 | 2.8661 | 0.32 | -0.18 | 0.15 | |
| 3.5 | 3.0059 | 0.25 | -0.12 | 0.09 | |
| 4 | 3.1152 | 0.19 | -0.09 | 0.06 | |
| 4.5 | 3.2029 | 0.16 | -0.06 | 0.04 | |
| 5 | 3.2749 | 0.13 | -0.05 | 0.03 | |
| 5.5 | 3.335 | 0.11 | -0.04 | 0.02 | |
| 6 | 3.3859 | 0.09 | -0.03 | 0.01 | |
| 6.5 | 3.4296 | 0.08 | -0.02 | 0.01 | |
| 7 | 3.4675 | 0.07 | -0.02 | 0.01 | |
| 7.5 | 3.5007 | 0.06 | -0.02 | 0.01 | |
| 8 | 3.53 | 0.06 | -0.01 | 0 | |
| 8.5 | 3.556 | 0.05 | -0.01 | 0 | |
| 9 | 3.5794 | 0.04 | -0.01 | 0 | |
| 9.5 | 3.6004 | 0.04 | -0.01 | 0 | |
| 10 | 3.6193 | 0.04 | -0.01 | 0 | |
| Graph: | |||||
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Graph(en) der Asymptote(n), Grenzkurve(n).
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