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Funktion: f(x) = ex-5·e0.5x+e-0.25x, Df = R, Wf = [-5.6214; +∞), reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 12.1488 | -3.06 | 0.75 | -0.19 | |
| -9.5 | 10.7078 | -2.71 | 0.66 | -0.17 | |
| -9 | 9.4323 | -2.4 | 0.58 | -0.16 | |
| -8.5 | 8.3018 | -2.13 | 0.51 | -0.14 | |
| -8 | 7.2978 | -1.89 | 0.44 | -0.13 | |
| -7.5 | 6.4038 | -1.69 | 0.38 | -0.12 | |
| -7 | 5.6045 | -1.51 | 0.32 | -0.11 | |
| -6.5 | 4.8861 | -1.37 | 0.27 | -0.1 | |
| -6 | 4.2352 | -1.24 | 0.22 | -0.1 | |
| -5.5 | 3.6395 | -1.14 | 0.17 | -0.1 | |
| -5 | 3.0867 | -1.07 | 0.12 | -0.1 | |
| -4.5 | 2.5643 | -1.02 | 0.07 | -0.1 | |
| -4 | 2.0599 | -1 | 0.02 | -0.11 | |
| -3.828 | 1.8882 | -1 | 0 | -0.11 | Wendepunkt W(-3.83|1.89) |
| -3.5 | 1.5602 | -1 | -0.04 | -0.12 | |
| -3 | 1.0511 | -1.04 | -0.1 | -0.12 | |
| -2.5 | 0.5178 | -1.1 | -0.16 | -0.13 | |
| -2.048 | 0.0018 | -1.19 | -0.22 | -0.12 | Nullstelle N(-2.05|0) |
| -2 | -0.0553 | -1.2 | -0.22 | -0.12 | |
| -1.5 | -0.6837 | -1.32 | -0.28 | -0.09 | |
| -1 | -1.3807 | -1.47 | -0.31 | -0.03 | |
| -0.5 | -2.1543 | -1.62 | -0.3 | 0.1 | |
| 0 | -3 | -1.75 | -0.19 | 0.36 | Schnittpunkt Sy(0|-3) |
| 0.368 | -3.6531 | -1.79 | 0 | 0.68 | Wendepunkt W(0.37|-3.65) |
| 0.5 | -3.8889 | -1.78 | 0.1 | 0.83 | |
| 1 | -4.7465 | -1.6 | 0.71 | 1.68 | |
| 1.5 | -5.416 | -0.98 | 1.88 | 3.15 | |
| 1.88 | -5.6214 | 0 | 3.39 | 4.95 | Tiefpunkt T(1.88|-5.62) |
| 2 | -5.5958 | 0.44 | 4.03 | 5.69 | |
| 2.5 | -4.734 | 3.32 | 7.85 | 10 | |
| 3 | -1.8505 | 8.76 | 14.51 | 17.3 | |
| 3.18 | 0 | 11.67 | 17.95 | 21 | Nullstelle N(3.18|0) |
| 3.5 | 4.7593 | 18.62 | 25.95 | 29.54 | |
| 4 | 18.0207 | 36.03 | 45.38 | 50.03 | |
| 4.5 | 42.9031 | 66.22 | 78.18 | 84.17 | |
| 5 | 87.7872 | 117.89 | 133.2 | 140.94 | |
| 5.5 | 166.7316 | 205.52 | 225.15 | 235.15 | |
| 6 | 303.2242 | 353.16 | 378.34 | 391.27 | |
| 6.5 | 536.3868 | 600.62 | 632.92 | 649.68 | |
| 7 | 931.2297 | 1013.8 | 1055.25 | 1077.02 | |
| 7.5 | 1595.5904 | 1701.7 | 1754.9 | 1783.26 | |
| 8 | 2708.1026 | 2844.43 | 2912.72 | 2949.8 | |
| 8.5 | 4564.3612 | 4739.48 | 4827.15 | 4875.85 | |
| 9 | 7653.1037 | 7878.02 | 7990.57 | 8054.9 | |
| 9.5 | 12781.8984 | 13070.75 | 13215.26 | 13300.82 | |
| 10 | 21284.4821 | 21655.43 | 21840.96 | 21955.7 | |
| 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