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Funktion: f(x) = -3x2/4 + 15x/8, Df = R, Wf = (-∞ 1.172], allgemeine Parabel (Normalform), Funktion achsensymmetrisch zur Senkrechten x = 1.25, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -93.75 | 16.87 | -1.5 | 0 | |
| -9.5 | -85.5 | 16.12 | -1.5 | 0 | |
| -9 | -77.625 | 15.37 | -1.5 | 0 | |
| -8.5 | -70.125 | 14.62 | -1.5 | 0 | |
| -8 | -63 | 13.88 | -1.5 | 0 | |
| -7.5 | -56.25 | 13.13 | -1.5 | 0 | |
| -7 | -49.875 | 12.38 | -1.5 | 0 | |
| -6.5 | -43.875 | 11.62 | -1.5 | 0 | |
| -6 | -38.25 | 10.88 | -1.5 | 0 | |
| -5.5 | -33 | 10.12 | -1.5 | 0 | |
| -5 | -28.125 | 9.38 | -1.5 | 0 | |
| -4.5 | -23.625 | 8.63 | -1.5 | 0 | |
| -4 | -19.5 | 7.88 | -1.5 | 0 | |
| -3.5 | -15.75 | 7.12 | -1.5 | 0 | |
| -3 | -12.375 | 6.37 | -1.5 | 0 | |
| -2.5 | -9.375 | 5.62 | -1.5 | 0 | |
| -2 | -6.75 | 4.88 | -1.5 | 0 | |
| -1.5 | -4.5 | 4.13 | -1.5 | 0 | |
| -1 | -2.625 | 3.37 | -1.5 | 0 | |
| -0.5 | -1.125 | 2.62 | -1.5 | 0 | |
| 0 | 0 | 1.88 | -1.5 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.5 | 0.75 | 1.13 | -1.5 | 0 | |
| 1 | 1.125 | 0.37 | -1.5 | 0 | |
| 1.25 | 1.1719 | 0 | -1.5 | 0 | Hochpunkt H(1.25|1.172) |
| 1.5 | 1.125 | -0.38 | -1.5 | 0 | |
| 2 | 0.75 | -1.12 | -1.5 | 0 | |
| 2.5 | 0 | -1.88 | -1.5 | 0 | Nullstelle N(2.5|0) |
| 3 | -1.125 | -2.63 | -1.5 | 0 | |
| 3.5 | -2.625 | -3.37 | -1.5 | 0 | |
| 4 | -4.5 | -4.13 | -1.5 | 0 | |
| 4.5 | -6.75 | -4.88 | -1.5 | 0 | |
| 5 | -9.375 | -5.63 | -1.5 | 0 | |
| 5.5 | -12.375 | -6.38 | -1.5 | 0 | |
| 6 | -15.75 | -7.13 | -1.5 | 0 | |
| 6.5 | -19.5 | -7.88 | -1.5 | 0 | |
| 7 | -23.625 | -8.63 | -1.5 | 0 | |
| 7.5 | -28.125 | -9.38 | -1.5 | 0 | |
| 8 | -33 | -10.12 | -1.5 | 0 | |
| 8.5 | -38.25 | -10.87 | -1.5 | 0 | |
| 9 | -43.875 | -11.62 | -1.5 | 0 | |
| 9.5 | -49.875 | -12.37 | -1.5 | 0 | |
| 10 | -56.25 | -13.13 | -1.5 | 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