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Funktion: f(x) = (ex-2·e-x)/3, Df = R, Wf = R, reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -14684.3105 | 14684.56 | -14684.43 | 14611.25 | |
| -9.5 | -8906.4845 | 8906.63 | -8906.56 | 8862.17 | |
| -9 | -5402.0559 | 5402.15 | -5402.1 | 5375.18 | |
| -8.5 | -3276.5125 | 3276.57 | -3276.54 | 3260.21 | |
| -8 | -1987.3052 | 1987.34 | -1987.32 | 1977.42 | |
| -7.5 | -1205.3614 | 1205.38 | -1205.37 | 1199.37 | |
| -7 | -731.0885 | 731.1 | -731.09 | 727.45 | |
| -6.5 | -443.4273 | 443.44 | -443.43 | 441.22 | |
| -6 | -268.9517 | 268.96 | -268.95 | 267.62 | |
| -5.5 | -163.1266 | 163.13 | -163.13 | 162.32 | |
| -5 | -98.9399 | 98.95 | -98.94 | 98.45 | |
| -4.5 | -60.0077 | 60.02 | -60.01 | 59.72 | |
| -4 | -36.3927 | 36.41 | -36.39 | 36.22 | |
| -3.5 | -22.0669 | 22.09 | -22.07 | 21.98 | |
| -3 | -13.3738 | 13.41 | -13.37 | 13.34 | |
| -2.5 | -8.0943 | 8.15 | -8.09 | 8.11 | |
| -2 | -4.8809 | 4.97 | -4.88 | 4.95 | |
| -1.5 | -2.9134 | 3.06 | -2.91 | 3.05 | |
| -1 | -1.6896 | 1.93 | -1.69 | 1.93 | |
| -0.5 | -0.897 | 1.3 | -0.9 | 1.3 | |
| 0 | -0.3333 | 1 | -0.33 | 1 | Schnittpunkt Sy(0|-0.33) |
| 0.34 | 0 | 0.94 | -0.01 | 0.94 | Nullstelle N(0.34|-0.01) = Wendepunkt W(0.34|0) |
| 0.5 | 0.1452 | 0.95 | 0.15 | 0.95 | |
| 1 | 0.6608 | 1.15 | 0.66 | 1.15 | |
| 1.5 | 1.3451 | 1.64 | 1.35 | 1.65 | |
| 2 | 2.3728 | 2.55 | 2.37 | 2.57 | |
| 2.5 | 4.0061 | 4.12 | 4.01 | 4.14 | |
| 3 | 6.662 | 6.73 | 6.66 | 6.76 | |
| 3.5 | 11.0184 | 11.06 | 11.02 | 11.11 | |
| 4 | 18.1872 | 18.21 | 18.19 | 18.3 | |
| 4.5 | 29.9983 | 30.01 | 30 | 30.16 | |
| 5 | 49.4666 | 49.48 | 49.47 | 49.72 | |
| 5.5 | 81.5613 | 81.57 | 81.56 | 81.98 | |
| 6 | 134.4746 | 134.48 | 134.48 | 135.15 | |
| 6.5 | 221.7129 | 221.72 | 221.71 | 222.83 | |
| 7 | 365.5438 | 365.55 | 365.55 | 367.38 | |
| 7.5 | 602.6804 | 602.69 | 602.69 | 605.71 | |
| 8 | 993.6524 | 993.67 | 993.66 | 998.65 | |
| 8.5 | 1638.2561 | 1638.28 | 1638.27 | 1646.49 | |
| 9 | 2701.0279 | 2701.07 | 2701.05 | 2714.6 | |
| 9.5 | 4453.2422 | 4453.32 | 4453.28 | 4475.62 | |
| 10 | 7342.1552 | 7342.28 | 7342.22 | 7379.05 | |
| 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