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Funktion: f(x) = (2x-x2)·e-0.1x2, Df = R, Wf = [-6.1366; 0.913], reelle Funktion, x -> -∞: f(x) -> 0 = y als Grenzkurve, x -> +∞: f(x) -> 0 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -0.0054 | -0.01 | -0.02 | -0.03 | |
| -9.5 | -0.0131 | -0.02 | -0.04 | -0.05 | |
| -9 | -0.0301 | -0.05 | -0.07 | -0.09 | |
| -8.5 | -0.065 | -0.1 | -0.13 | -0.15 | |
| -8 | -0.1329 | -0.18 | -0.22 | -0.22 | |
| -7.5 | -0.257 | -0.32 | -0.35 | -0.29 | |
| -7 | -0.4691 | -0.54 | -0.51 | -0.33 | |
| -6.5 | -0.808 | -0.83 | -0.66 | -0.28 | |
| -6 | -1.3115 | -1.19 | -0.76 | -0.09 | |
| -5.5 | -2.003 | -1.57 | -0.73 | 0.25 | |
| -5 | -2.873 | -1.89 | -0.49 | 0.73 | |
| -4.5 | -3.8608 | -2.02 | 0 | 1.22 | Wendepunkt W(-4.5|-3.86) |
| -4 | -4.8455 | -1.86 | 0.69 | 1.54 | |
| -3.5 | -5.6548 | -1.31 | 1.47 | 1.5 | |
| -3 | -6.0985 | -0.41 | 2.11 | 0.97 | |
| -2.82 | -6.1366 | 0 | 2.26 | 0.66 | Tiefpunkt T(-2.82|-6.14) |
| -2.5 | -6.0217 | 0.74 | 2.38 | 0 | |
| -2 | -5.3626 | 1.88 | 2.09 | -1.16 | |
| -1.5 | -4.1922 | 2.73 | 1.26 | -2.12 | |
| -1 | -2.7145 | 3.08 | 0.07 | -2.52 | |
| -0.98 | -2.653 | 3.08 | 0 | -2.52 | Wendepunkt W(-0.98|-2.65) |
| -0.5 | -1.2191 | 2.8 | -1.13 | -2.17 | |
| 0 | 0 | 2 | -2 | -1.19 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.5 | 0.7315 | 0.9 | -2.28 | 0.09 | |
| 0.9 | 0.913 | 0 | -2.06 | 1.01 | Hochpunkt H(0.9|0.91) |
| 1 | 0.9048 | -0.18 | -1.95 | 1.2 | |
| 1.5 | 0.5989 | -0.98 | -1.18 | 1.8 | |
| 2 | 0 | -1.34 | -0.27 | 1.77 | Nullstelle N(2|0) |
| 2.15 | -0.2031 | -1.36 | 0 | 1.65 | Wendepunkt W(2.15|-0.2) |
| 2.5 | -0.6691 | -1.27 | 0.5 | 1.24 | |
| 3 | -1.2197 | -0.89 | 0.94 | 0.5 | |
| 3.5 | -1.5422 | -0.39 | 1.02 | -0.17 | |
| 3.9 | -1.619 | 0 | 0.88 | -0.52 | Tiefpunkt T(3.9|-1.62) |
| 4 | -1.6152 | 0.08 | 0.82 | -0.58 | |
| 4.5 | -1.4849 | 0.41 | 0.49 | -0.7 | |
| 5 | -1.2313 | 0.57 | 0.16 | -0.59 | |
| 5.31 | -1.048 | 0.6 | 0 | -0.46 | Wendepunkt W(5.31|-1.05) |
| 5.5 | -0.9347 | 0.59 | -0.08 | -0.37 | |
| 6 | -0.6558 | 0.51 | -0.21 | -0.16 | |
| 6.5 | -0.4278 | 0.4 | -0.25 | 0 | |
| 7 | -0.2606 | 0.28 | -0.22 | 0.09 | |
| 7.5 | -0.1488 | 0.18 | -0.17 | 0.11 | |
| 8 | -0.0798 | 0.1 | -0.12 | 0.1 | |
| 8.5 | -0.0402 | 0.06 | -0.07 | 0.08 | |
| 9 | -0.0191 | 0.03 | -0.04 | 0.05 | |
| 9.5 | -0.0086 | 0.01 | -0.02 | 0.03 | |
| 10 | -0.0036 | 0.01 | -0.01 | 0.02 | |
| 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