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Funktion: f(x) = -x2 + 6x + 7, Df = R, Wf = (-∞; 16], allgemeine Parabel (Normalform; Scheitelform: f(x) = -(x-3)2 + 16), Funktion achsensymmetrisch zur Senkrechten x = 3, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -153 | 26 | -2 | 0 | |
| -9.5 | -140.25 | 25 | -2 | 0 | |
| -9 | -128 | 24 | -2 | 0 | |
| -8.5 | -116.25 | 23 | -2 | 0 | |
| -8 | -105 | 22 | -2 | 0 | |
| -7.5 | -94.25 | 21 | -2 | 0 | |
| -7 | -84 | 20 | -2 | 0 | |
| -6.5 | -74.25 | 19 | -2 | 0 | |
| -6 | -65 | 18 | -2 | 0 | |
| -5.5 | -56.25 | 17 | -2 | 0 | |
| -5 | -48 | 16 | -2 | 0 | |
| -4.5 | -40.25 | 15 | -2 | 0 | |
| -4 | -33 | 14 | -2 | 0 | |
| -3.5 | -26.25 | 13 | -2 | 0 | |
| -3 | -20 | 12 | -2 | 0 | |
| -2.5 | -14.25 | 11 | -2 | 0 | |
| -2 | -9 | 10 | -2 | 0 | |
| -1.5 | -4.25 | 9 | -2 | 0 | |
| -1 | 0 | 8 | -2 | 0 | Nullstelle N(-1|0) |
| -0.5 | 3.75 | 7 | -2 | 0 | |
| 0 | 7 | 6 | -2 | 0 | Schnittpunkt Sy(0|7) |
| 0.5 | 9.75 | 5 | -2 | 0 | |
| 1 | 12 | 4 | -2 | 0 | |
| 1.5 | 13.75 | 3 | -2 | 0 | |
| 2 | 15 | 2 | -2 | 0 | |
| 2.5 | 15.75 | 1 | -2 | 0 | |
| 3 | 16 | 0 | -2 | 0 | Hochpunkt H(3|16) |
| 3.5 | 15.75 | -1 | -2 | 0 | |
| 4 | 15 | -2 | -2 | 0 | |
| 4.5 | 13.75 | -3 | -2 | 0 | |
| 5 | 12 | -4 | -2 | 0 | |
| 5.5 | 9.75 | -5 | -2 | 0 | |
| 6 | 7 | -6 | -2 | 0 | |
| 6.5 | 3.75 | -7 | -2 | 0 | |
| 7 | 0 | -8 | -2 | 0 | Nullstelle N(7|0) |
| 7.5 | -4.25 | -9 | -2 | 0 | |
| 8 | -9 | -10 | -2 | 0 | |
| 8.5 | -14.25 | -11 | -2 | 0 | |
| 9 | -20 | -12 | -2 | 0 | |
| 9.5 | -26.25 | -13 | -2 | 0 | |
| 10 | -33 | -14 | -2 | 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