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Funktion: f(x) = 0.56·(x-2.85)2, Df = R, Wf = [0; +∞), allgemeine Parabel (Scheitelform), Funktion achsensymmetrisch zur Senkrechten x = 2.85, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 92.4686 | -14.39 | 1.12 | 0 | |
| -9.5 | 85.4126 | -13.83 | 1.12 | 0 | |
| -9 | 78.6366 | -13.27 | 1.12 | 0 | |
| -8.5 | 72.1406 | -12.71 | 1.12 | 0 | |
| -8 | 65.9246 | -12.15 | 1.12 | 0 | |
| -7.5 | 59.9886 | -11.59 | 1.12 | 0 | |
| -7 | 54.3326 | -11.03 | 1.12 | 0 | |
| -6.5 | 48.9566 | -10.47 | 1.12 | 0 | |
| -6 | 43.8606 | -9.91 | 1.12 | 0 | |
| -5.5 | 39.0446 | -9.35 | 1.12 | 0 | |
| -5 | 34.5086 | -8.79 | 1.12 | 0 | |
| -4.5 | 30.2526 | -8.23 | 1.12 | 0 | |
| -4 | 26.2766 | -7.67 | 1.12 | 0 | |
| -3.5 | 22.5806 | -7.11 | 1.12 | 0 | |
| -3 | 19.1646 | -6.55 | 1.12 | 0 | |
| -2.5 | 16.0286 | -5.99 | 1.12 | 0 | |
| -2 | 13.1726 | -5.43 | 1.12 | 0 | |
| -1.5 | 10.5966 | -4.87 | 1.12 | 0 | |
| -1 | 8.3006 | -4.31 | 1.12 | 0 | |
| -0.5 | 6.2846 | -3.75 | 1.12 | 0 | |
| 0 | 4.5486 | -3.19 | 1.12 | 0 | Schnittpunkt Sy(0|4.55) |
| 0.5 | 3.0926 | -2.63 | 1.12 | 0 | |
| 1 | 1.9166 | -2.07 | 1.12 | 0 | |
| 1.5 | 1.0206 | -1.51 | 1.12 | 0 | |
| 2 | 0.4046 | -0.95 | 1.12 | 0 | |
| 2.5 | 0.0686 | -0.39 | 1.12 | 0 | |
| 2.85 | 0 | 0 | 1.12 | 0 | Nullstelle N(2.85|0) = Tiefpunkt T(2.85|0) |
| 3 | 0.0126 | 0.17 | 1.12 | 0 | |
| 3.5 | 0.2366 | 0.73 | 1.12 | 0 | |
| 4 | 0.7406 | 1.29 | 1.12 | 0 | |
| 4.5 | 1.5246 | 1.85 | 1.12 | 0 | |
| 5 | 2.5886 | 2.41 | 1.12 | 0 | |
| 5.5 | 3.9326 | 2.97 | 1.12 | 0 | |
| 6 | 5.5566 | 3.53 | 1.12 | 0 | |
| 6.5 | 7.4606 | 4.09 | 1.12 | 0 | |
| 7 | 9.6446 | 4.65 | 1.12 | 0 | |
| 7.5 | 12.1086 | 5.21 | 1.12 | 0 | |
| 8 | 14.8526 | 5.77 | 1.12 | 0 | |
| 8.5 | 17.8766 | 6.33 | 1.12 | 0 | |
| 9 | 21.1806 | 6.89 | 1.12 | 0 | |
| 9.5 | 24.7646 | 7.45 | 1.12 | 0 | |
| 10 | 28.6286 | 8.01 | 1.12 | 0 | |
| 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, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann