www.michael-buhlmann.de
Funktion: f(x) = -1.2·(x+3.5)2 + 5.4, Df = R, Wf = (-∞; 5.4], allgemeine Parabel (Scheitelform), Funktion achsensymmetrisch zur Senkrechten x = -3.5, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -45.3 | 15.6 | -2.4 | 0 | |
| -9.5 | -37.8 | 14.4 | -2.4 | 0 | |
| -9 | -30.9 | 13.2 | -2.4 | 0 | |
| -8.5 | -24.6 | 12 | -2.4 | 0 | |
| -8 | -18.9 | 10.8 | -2.4 | 0 | |
| -7.5 | -13.8 | 9.6 | -2.4 | 0 | |
| -7 | -9.3 | 8.4 | -2.4 | 0 | |
| -6.5 | -5.4 | 7.2 | -2.4 | 0 | |
| -6 | -2.1 | 6 | -2.4 | 0 | |
| -5.622 | 0 | 5.09 | -2.4 | 0 | Nullstelle N(-5.62|0) |
| -5.5 | 0.6 | 4.8 | -2.4 | 0 | |
| -5 | 2.7 | 3.6 | -2.4 | 0 | |
| -4.5 | 4.2 | 2.4 | -2.4 | 0 | |
| -4 | 5.1 | 1.2 | -2.4 | 0 | |
| -3.5 | 5.4 | 0 | -2.4 | 0 | Hochpunkt H(-3.5|5.4) |
| -3 | 5.1 | -1.2 | -2.4 | 0 | |
| -2.5 | 4.2 | -2.4 | -2.4 | 0 | |
| -2 | 2.7 | -3.6 | -2.4 | 0 | |
| -1.5 | 0.6 | -4.8 | -2.4 | 0 | |
| -1.38 | 0 | -5.09 | -2.4 | 0 | Nullstelle N(-1.38|0.01) |
| -1 | -2.1 | -6 | -2.4 | 0 | |
| -0.5 | -5.4 | -7.2 | -2.4 | 0 | |
| 0 | -9.3 | -8.4 | -2.4 | 0 | Schnittpunkt Sy(0|-9.3) |
| 0.5 | -13.8 | -9.6 | -2.4 | 0 | |
| 1 | -18.9 | -10.8 | -2.4 | 0 | |
| 1.5 | -24.6 | -12 | -2.4 | 0 | |
| 2 | -30.9 | -13.2 | -2.4 | 0 | |
| 2.5 | -37.8 | -14.4 | -2.4 | 0 | |
| 3 | -45.3 | -15.6 | -2.4 | 0 | |
| 3.5 | -53.4 | -16.8 | -2.4 | 0 | |
| 4 | -62.1 | -18 | -2.4 | 0 | |
| 4.5 | -71.4 | -19.2 | -2.4 | 0 | |
| 5 | -81.3 | -20.4 | -2.4 | 0 | |
| 5.5 | -91.8 | -21.6 | -2.4 | 0 | |
| 6 | -102.9 | -22.8 | -2.4 | 0 | |
| 6.5 | -114.6 | -24 | -2.4 | 0 | |
| 7 | -126.9 | -25.2 | -2.4 | 0 | |
| 7.5 | -139.8 | -26.4 | -2.4 | 0 | |
| 8 | -153.3 | -27.6 | -2.4 | 0 | |
| 8.5 | -167.4 | -28.8 | -2.4 | 0 | |
| 9 | -182.1 | -30 | -2.4 | 0 | |
| 9.5 | -197.4 | -31.2 | -2.4 | 0 | |
| 10 | -213.3 | -32.4 | -2.4 | 0 | |
| Graph: | |||||
| |||||
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