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Funktion: f(x) = (ex+e-x)/10, Df = R, Wf = [0.2; +∞), reelle Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 2202.6466 | -2202.68 | 2202.66 | -2191.69 | |
| -9.5 | 1335.9727 | -1335.99 | 1335.98 | -1329.33 | |
| -9 | 810.3084 | -810.32 | 810.32 | -806.28 | |
| -8.5 | 491.4769 | -491.49 | 491.48 | -489.03 | |
| -8 | 298.0958 | -298.1 | 298.1 | -296.61 | |
| -7.5 | 180.8043 | -180.81 | 180.81 | -179.9 | |
| -7 | 109.6634 | -109.67 | 109.66 | -109.12 | |
| -6.5 | 66.5143 | -66.52 | 66.51 | -66.18 | |
| -6 | 40.3431 | -40.34 | 40.34 | -40.14 | |
| -5.5 | 24.4696 | -24.47 | 24.47 | -24.35 | |
| -5 | 14.842 | -14.84 | 14.84 | -14.77 | |
| -4.5 | 9.0028 | -9 | 9 | -8.96 | |
| -4 | 5.4616 | -5.46 | 5.46 | -5.43 | |
| -3.5 | 3.3146 | -3.31 | 3.31 | -3.29 | |
| -3 | 2.0135 | -2 | 2.01 | -1.99 | |
| -2.5 | 1.2265 | -1.21 | 1.23 | -1.2 | |
| -2 | 0.7524 | -0.73 | 0.75 | -0.72 | |
| -1.5 | 0.4705 | -0.43 | 0.47 | -0.42 | |
| -1 | 0.3086 | -0.24 | 0.31 | -0.23 | |
| -0.5 | 0.2255 | -0.1 | 0.23 | -0.1 | |
| 0 | 0.2 | 0 | 0.2 | 0 | Schnittpunkt Sy(0|0.2) = Tiefpunkt T(0|0.2) |
| 0.5 | 0.2255 | 0.1 | 0.23 | 0.11 | |
| 1 | 0.3086 | 0.24 | 0.31 | 0.24 | |
| 1.5 | 0.4705 | 0.43 | 0.47 | 0.43 | |
| 2 | 0.7524 | 0.73 | 0.75 | 0.73 | |
| 2.5 | 1.2265 | 1.21 | 1.23 | 1.22 | |
| 3 | 2.0135 | 2 | 2.01 | 2.01 | |
| 3.5 | 3.3146 | 3.31 | 3.31 | 3.33 | |
| 4 | 5.4616 | 5.46 | 5.46 | 5.49 | |
| 4.5 | 9.0028 | 9 | 9 | 9.05 | |
| 5 | 14.842 | 14.84 | 14.84 | 14.92 | |
| 5.5 | 24.4696 | 24.47 | 24.47 | 24.59 | |
| 6 | 40.3431 | 40.34 | 40.34 | 40.55 | |
| 6.5 | 66.5143 | 66.52 | 66.51 | 66.85 | |
| 7 | 109.6634 | 109.67 | 109.66 | 110.21 | |
| 7.5 | 180.8043 | 180.81 | 180.81 | 181.71 | |
| 8 | 298.0958 | 298.1 | 298.1 | 299.59 | |
| 8.5 | 491.4769 | 491.49 | 491.48 | 493.95 | |
| 9 | 810.3084 | 810.32 | 810.32 | 814.38 | |
| 9.5 | 1335.9727 | 1335.99 | 1335.98 | 1342.69 | |
| 10 | 2202.6466 | 2202.68 | 2202.66 | 2213.72 | |
| 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