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Funktion: f(x) = (2x-3)(x-5)·ex2/12, Df = R, Wf = [-19.009; +∞), reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -6 | 3314.1136 | -4057.41 | 5433.24 | -7754.12 | |
| -5.5 | 1828.5268 | -2111.57 | 2689.19 | -3671.6 | |
| -5 | 1044.0553 | -1135.11 | 1372.91 | -1791.6 | |
| -4.5 | 616.2782 | -629.81 | 722.38 | -900.28 | |
| -4 | 375.5731 | -360.41 | 391.39 | -465.51 | |
| -3.5 | 235.9181 | -212.56 | 218.13 | -247.51 | |
| -3 | 152.424 | -129.14 | 124.9 | -135.22 | |
| -2.5 | 101.0058 | -80.81 | 73.37 | -75.86 | |
| -2 | 68.385 | -52.1 | 44.12 | -43.7 | |
| -1.5 | 47.043 | -34.68 | 27.07 | -25.86 | |
| -1 | 32.6071 | -23.91 | 16.85 | -15.74 | |
| -0.5 | 22.4631 | -17.19 | 10.54 | -9.9 | |
| 0 | 15 | -13 | 6.5 | -6.47 | Schnittpunkt Sy(0|15) |
| 0.5 | 9.1895 | -10.47 | 3.81 | -4.42 | |
| 1 | 4.3476 | -9.06 | 1.93 | -3.14 | |
| 1.5 | 0 | -8.44 | 0.6 | -2.18 | Nullstelle N(1.5|0) |
| 1.82 | -2.6822 | -8.35 | 0 | -1.52 | Wendepunkt W(1.82|-2.68) |
| 2 | -4.1868 | -8.37 | -0.23 | -1.07 | |
| 2.5 | -8.4171 | -8.56 | -0.34 | 0.93 | |
| 2.71 | -10.2198 | -8.6 | 0 | 2.36 | Wendepunkt W(2.71|-10.22) |
| 3 | -12.702 | -8.47 | 1.06 | 5.36 | |
| 3.5 | -16.653 | -6.94 | 5.9 | 15.64 | |
| 4 | -18.9683 | -1.26 | 18.76 | 39.63 | |
| 4.06 | -19.009 | 0 | 21.25 | 44.12 | Tiefpunkt T(4.06|-19.01) |
| 4.5 | -16.2178 | 14.87 | 50.34 | 95.69 | |
| 5 | 0 | 56.22 | 125.83 | 227.51 | Nullstelle N(5|0) |
| 5.5 | 49.7558 | 157.57 | 305.11 | 540.84 | |
| 6 | 180.7698 | 401.73 | 733.14 | 1296.9 | |
| 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