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Funktion: f(x) = e0.5x-5·e0.25x+4, Df = [-2.25; +∞), Wf = R, reelle Funktion, x -> -∞: f(x) -> 4 = y als Grenzkurve, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 3.5963 | -0.1 | -0.02 | -0.01 | |
| -9.5 | 3.5436 | -0.11 | -0.03 | -0.01 | |
| -9 | 3.4841 | -0.13 | -0.03 | -0.01 | |
| -8.5 | 3.4171 | -0.14 | -0.03 | -0.01 | |
| -8 | 3.3416 | -0.16 | -0.04 | -0.01 | |
| -7.5 | 3.2567 | -0.18 | -0.04 | -0.01 | |
| -7 | 3.1613 | -0.2 | -0.05 | -0.01 | |
| -6.5 | 3.0542 | -0.23 | -0.05 | -0.01 | |
| -6 | 2.9341 | -0.25 | -0.06 | -0.01 | |
| -5.5 | 2.7997 | -0.28 | -0.06 | -0.01 | |
| -5 | 2.6496 | -0.32 | -0.07 | -0.01 | |
| -4.5 | 2.4821 | -0.35 | -0.08 | -0.01 | |
| -4 | 2.2959 | -0.39 | -0.08 | -0.01 | |
| -3.5 | 2.0895 | -0.43 | -0.09 | -0.01 | |
| -3 | 1.8613 | -0.48 | -0.09 | -0.01 | |
| -2.5 | 1.6102 | -0.53 | -0.1 | -0.01 | |
| -2 | 1.3352 | -0.57 | -0.1 | 0 | |
| -1.5 | 1.0359 | -0.62 | -0.1 | 0.01 | |
| -1 | 0.7125 | -0.67 | -0.09 | 0.02 | |
| -0.5 | 0.3663 | -0.71 | -0.08 | 0.03 | |
| 0 | 0 | -0.75 | -0.06 | 0.05 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.5 | -0.3817 | -0.77 | -0.03 | 0.07 | |
| 0.89 | -0.6855 | -0.78 | 0 | 0.1 | Wendepunkt W(0.89|-0.69) |
| 1 | -0.7714 | -0.78 | 0.01 | 0.11 | |
| 1.5 | -1.158 | -0.76 | 0.07 | 0.15 | |
| 2 | -1.5253 | -0.7 | 0.16 | 0.21 | |
| 2.5 | -1.8509 | -0.59 | 0.29 | 0.29 | |
| 3 | -2.1033 | -0.41 | 0.46 | 0.4 | |
| 3.5 | -2.2398 | -0.12 | 0.69 | 0.53 | |
| 3.66 | -2.25 | 0 | 0.78 | 0.59 | Tiefpunkt T(3.66|-2.25) |
| 4 | -2.2024 | 0.3 | 1 | 0.71 | |
| 4.5 | -1.9133 | 0.89 | 1.41 | 0.95 | |
| 5 | -1.2692 | 1.73 | 1.95 | 1.25 | |
| 5.5 | -0.1328 | 2.88 | 2.67 | 1.65 | |
| 5.54 | 0 | 2.99 | 2.74 | 1.69 | Nullstelle N(5.54|0) |
| 6 | 1.6771 | 4.44 | 3.62 | 2.17 | |
| 6.5 | 4.3982 | 6.55 | 4.86 | 2.83 | |
| 7 | 8.3424 | 9.36 | 6.48 | 3.7 | |
| 7.5 | 13.917 | 13.11 | 8.59 | 4.82 | |
| 8 | 21.6529 | 18.06 | 11.34 | 6.26 | |
| 8.5 | 32.2409 | 24.59 | 14.91 | 8.13 | |
| 9 | 46.5785 | 33.15 | 19.54 | 10.54 | |
| 9.5 | 65.8292 | 44.35 | 25.54 | 13.64 | |
| 10 | 91.5007 | 58.98 | 33.3 | 17.65 | |
| 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