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Funktion: f(x) = -1.5·x2, Df = R, Wf = (-∞; 0], allgemeine Parabel als gestreckte Normalparabel, um die x-Achse gespiegelt, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -150 | 30 | -3 | 0 | |
| -9.5 | -135.375 | 28.5 | -3 | 0 | |
| -9 | -121.5 | 27 | -3 | 0 | |
| -8.5 | -108.375 | 25.5 | -3 | 0 | |
| -8 | -96 | 24 | -3 | 0 | |
| -7.5 | -84.375 | 22.5 | -3 | 0 | |
| -7 | -73.5 | 21 | -3 | 0 | |
| -6.5 | -63.375 | 19.5 | -3 | 0 | |
| -6 | -54 | 18 | -3 | 0 | |
| -5.5 | -45.375 | 16.5 | -3 | 0 | |
| -5 | -37.5 | 15 | -3 | 0 | |
| -4.5 | -30.375 | 13.5 | -3 | 0 | |
| -4 | -24 | 12 | -3 | 0 | |
| -3.5 | -18.375 | 10.5 | -3 | 0 | |
| -3 | -13.5 | 9 | -3 | 0 | |
| -2.5 | -9.375 | 7.5 | -3 | 0 | |
| -2 | -6 | 6 | -3 | 0 | |
| -1.5 | -3.375 | 4.5 | -3 | 0 | |
| -1 | -1.5 | 3 | -3 | 0 | |
| -0.5 | -0.375 | 1.5 | -3 | 0 | |
| 0 | 0 | 0 | -3 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Hochpunkt H(0|0) |
| 0.5 | -0.375 | -1.5 | -3 | 0 | |
| 1 | -1.5 | -3 | -3 | 0 | |
| 1.5 | -3.375 | -4.5 | -3 | 0 | |
| 2 | -6 | -6 | -3 | 0 | |
| 2.5 | -9.375 | -7.5 | -3 | 0 | |
| 3 | -13.5 | -9 | -3 | 0 | |
| 3.5 | -18.375 | -10.5 | -3 | 0 | |
| 4 | -24 | -12 | -3 | 0 | |
| 4.5 | -30.375 | -13.5 | -3 | 0 | |
| 5 | -37.5 | -15 | -3 | 0 | |
| 5.5 | -45.375 | -16.5 | -3 | 0 | |
| 6 | -54 | -18 | -3 | 0 | |
| 6.5 | -63.375 | -19.5 | -3 | 0 | |
| 7 | -73.5 | -21 | -3 | 0 | |
| 7.5 | -84.375 | -22.5 | -3 | 0 | |
| 8 | -96 | -24 | -3 | 0 | |
| 8.5 | -108.375 | -25.5 | -3 | 0 | |
| 9 | -121.5 | -27 | -3 | 0 | |
| 9.5 | -135.375 | -28.5 | -3 | 0 | |
| 10 | -150 | -30 | -3 | 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