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Funktion: f(x) = 1.4·x2 - 2.2·x - 3.8, Df = R, Wf = [-4.6643; +∞), allgemeine Parabel (Normalform), Funktion achsensymmetrisch zur Senkrechten x = 0.784, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 158.2 | -30.2 | 2.8 | 0 | |
| -9.5 | 143.45 | -28.8 | 2.8 | 0 | |
| -9 | 129.4 | -27.4 | 2.8 | 0 | |
| -8.5 | 116.05 | -26 | 2.8 | 0 | |
| -8 | 103.4 | -24.6 | 2.8 | 0 | |
| -7.5 | 91.45 | -23.2 | 2.8 | 0 | |
| -7 | 80.2 | -21.8 | 2.8 | 0 | |
| -6.5 | 69.65 | -20.4 | 2.8 | 0 | |
| -6 | 59.8 | -19 | 2.8 | 0 | |
| -5.5 | 50.65 | -17.6 | 2.8 | 0 | |
| -5 | 42.2 | -16.2 | 2.8 | 0 | |
| -4.5 | 34.45 | -14.8 | 2.8 | 0 | |
| -4 | 27.4 | -13.4 | 2.8 | 0 | |
| -3.5 | 21.05 | -12 | 2.8 | 0 | |
| -3 | 15.4 | -10.6 | 2.8 | 0 | |
| -2.5 | 10.45 | -9.2 | 2.8 | 0 | |
| -2 | 6.2 | -7.8 | 2.8 | 0 | |
| -1.5 | 2.65 | -6.4 | 2.8 | 0 | |
| -1.04 | 0 | -5.11 | 2.8 | 0 | Nullstelle N(-1.04|0) |
| -1 | -0.2 | -5 | 2.8 | 0 | |
| -0.5 | -2.35 | -3.6 | 2.8 | 0 | |
| 0 | -3.8 | -2.2 | 2.8 | 0 | Schnittpunkt Sy(0|-3.8) |
| 0.5 | -4.55 | -0.8 | 2.8 | 0 | |
| 0.784 | -4.6643 | 0 | 2.8 | 0 | Tiefpunkt T(0.78|-4.66) |
| 1 | -4.6 | 0.6 | 2.8 | 0 | |
| 1.5 | -3.95 | 2 | 2.8 | 0 | |
| 2 | -2.6 | 3.4 | 2.8 | 0 | |
| 2.5 | -0.55 | 4.8 | 2.8 | 0 | |
| 2.61 | 0 | 5.11 | 2.8 | 0 | Nullstelle N(2.61|0) |
| 3 | 2.2 | 6.2 | 2.8 | 0 | |
| 3.5 | 5.65 | 7.6 | 2.8 | 0 | |
| 4 | 9.8 | 9 | 2.8 | 0 | |
| 4.5 | 14.65 | 10.4 | 2.8 | 0 | |
| 5 | 20.2 | 11.8 | 2.8 | 0 | |
| 5.5 | 26.45 | 13.2 | 2.8 | 0 | |
| 6 | 33.4 | 14.6 | 2.8 | 0 | |
| 6.5 | 41.05 | 16 | 2.8 | 0 | |
| 7 | 49.4 | 17.4 | 2.8 | 0 | |
| 7.5 | 58.45 | 18.8 | 2.8 | 0 | |
| 8 | 68.2 | 20.2 | 2.8 | 0 | |
| 8.5 | 78.65 | 21.6 | 2.8 | 0 | |
| 9 | 89.8 | 23 | 2.8 | 0 | |
| 9.5 | 101.65 | 24.4 | 2.8 | 0 | |
| 10 | 114.2 | 25.8 | 2.8 | 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