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Funktion: f(x) = -2x2 + x + 3, Df = R, Wf = (-∞; 3.125], allgemeine Parabel (Normalform), Funktion achsensymmetrisch zur Senkrechten x = 0.25, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -207 | 41 | -4 | 0 | |
| -9.5 | -187 | 39 | -4 | 0 | |
| -9 | -168 | 37 | -4 | 0 | |
| -8.5 | -150 | 35 | -4 | 0 | |
| -8 | -133 | 33 | -4 | 0 | |
| -7.5 | -117 | 31 | -4 | 0 | |
| -7 | -102 | 29 | -4 | 0 | |
| -6.5 | -88 | 27 | -4 | 0 | |
| -6 | -75 | 25 | -4 | 0 | |
| -5.5 | -63 | 23 | -4 | 0 | |
| -5 | -52 | 21 | -4 | 0 | |
| -4.5 | -42 | 19 | -4 | 0 | |
| -4 | -33 | 17 | -4 | 0 | |
| -3.5 | -25 | 15 | -4 | 0 | |
| -3 | -18 | 13 | -4 | 0 | |
| -2.5 | -12 | 11 | -4 | 0 | |
| -2 | -7 | 9 | -4 | 0 | |
| -1.5 | -3 | 7 | -4 | 0 | |
| -1 | 0 | 5 | -4 | 0 | Nullstelle N(-1|0) |
| -0.5 | 2 | 3 | -4 | 0 | |
| 0 | 3 | 1 | -4 | 0 | Schnittpunkt Sy(0|3) |
| 0.25 | 3.125 | 0 | -4 | 0 | Hochpunkt H(0.25|3.125) |
| 0.5 | 3 | -1 | -4 | 0 | |
| 1 | 2 | -3 | -4 | 0 | |
| 1.5 | 0 | -5 | -4 | 0 | Nullstelle N(1.5|0) |
| 2 | -3 | -7 | -4 | 0 | |
| 2.5 | -7 | -9 | -4 | 0 | |
| 3 | -12 | -11 | -4 | 0 | |
| 3.5 | -18 | -13 | -4 | 0 | |
| 4 | -25 | -15 | -4 | 0 | |
| 4.5 | -33 | -17 | -4 | 0 | |
| 5 | -42 | -19 | -4 | 0 | |
| 5.5 | -52 | -21 | -4 | 0 | |
| 6 | -63 | -23 | -4 | 0 | |
| 6.5 | -75 | -25 | -4 | 0 | |
| 7 | -88 | -27 | -4 | 0 | |
| 7.5 | -102 | -29 | -4 | 0 | |
| 8 | -117 | -31 | -4 | 0 | |
| 8.5 | -133 | -33 | -4 | 0 | |
| 9 | -150 | -35 | -4 | 0 | |
| 9.5 | -168 | -37 | -4 | 0 | |
| 10 | -187 | -39 | -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