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Funktion: f(x) = 2x2, Df = R, Wf = [0; +∞), allgemeine Parabel als gestreckte Normalparabel, 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 | 200 | -40 | 4 | 0 | |
| -9.5 | 180.5 | -38 | 4 | 0 | |
| -9 | 162 | -36 | 4 | 0 | |
| -8.5 | 144.5 | -34 | 4 | 0 | |
| -8 | 128 | -32 | 4 | 0 | |
| -7.5 | 112.5 | -30 | 4 | 0 | |
| -7 | 98 | -28 | 4 | 0 | |
| -6.5 | 84.5 | -26 | 4 | 0 | |
| -6 | 72 | -24 | 4 | 0 | |
| -5.5 | 60.5 | -22 | 4 | 0 | |
| -5 | 50 | -20 | 4 | 0 | |
| -4.5 | 40.5 | -18 | 4 | 0 | |
| -4 | 32 | -16 | 4 | 0 | |
| -3.5 | 24.5 | -14 | 4 | 0 | |
| -3 | 18 | -12 | 4 | 0 | |
| -2.5 | 12.5 | -10 | 4 | 0 | |
| -2 | 8 | -8 | 4 | 0 | |
| -1.5 | 4.5 | -6 | 4 | 0 | |
| -1 | 2 | -4 | 4 | 0 | |
| -0.5 | 0.5 | -2 | 4 | 0 | |
| 0 | 0 | 0 | 4 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
| 0.5 | 0.5 | 2 | 4 | 0 | |
| 1 | 2 | 4 | 4 | 0 | |
| 1.5 | 4.5 | 6 | 4 | 0 | |
| 2 | 8 | 8 | 4 | 0 | |
| 2.5 | 12.5 | 10 | 4 | 0 | |
| 3 | 18 | 12 | 4 | 0 | |
| 3.5 | 24.5 | 14 | 4 | 0 | |
| 4 | 32 | 16 | 4 | 0 | |
| 4.5 | 40.5 | 18 | 4 | 0 | |
| 5 | 50 | 20 | 4 | 0 | |
| 5.5 | 60.5 | 22 | 4 | 0 | |
| 6 | 72 | 24 | 4 | 0 | |
| 6.5 | 84.5 | 26 | 4 | 0 | |
| 7 | 98 | 28 | 4 | 0 | |
| 7.5 | 112.5 | 30 | 4 | 0 | |
| 8 | 128 | 32 | 4 | 0 | |
| 8.5 | 144.5 | 34 | 4 | 0 | |
| 9 | 162 | 36 | 4 | 0 | |
| 9.5 | 180.5 | 38 | 4 | 0 | |
| 10 | 200 | 40 | 4 | 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