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Funktion: f(x) = -0.35·x2 - 0.7·x - 1.1, Df = R, Wf = (-∞; -0.75], allgemeine Parabel (Normalform), Funktion achsensymmetrisch zur Senkrechten x = -1, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -29.1 | 6.3 | -0.7 | 0 | |
| -9.5 | -26.0375 | 5.95 | -0.7 | 0 | |
| -9 | -23.15 | 5.6 | -0.7 | 0 | |
| -8.5 | -20.4375 | 5.25 | -0.7 | 0 | |
| -8 | -17.9 | 4.9 | -0.7 | 0 | |
| -7.5 | -15.5375 | 4.55 | -0.7 | 0 | |
| -7 | -13.35 | 4.2 | -0.7 | 0 | |
| -6.5 | -11.3375 | 3.85 | -0.7 | 0 | |
| -6 | -9.5 | 3.5 | -0.7 | 0 | |
| -5.5 | -7.8375 | 3.15 | -0.7 | 0 | |
| -5 | -6.35 | 2.8 | -0.7 | 0 | |
| -4.5 | -5.0375 | 2.45 | -0.7 | 0 | |
| -4 | -3.9 | 2.1 | -0.7 | 0 | |
| -3.5 | -2.9375 | 1.75 | -0.7 | 0 | |
| -3 | -2.15 | 1.4 | -0.7 | 0 | |
| -2.5 | -1.5375 | 1.05 | -0.7 | 0 | |
| -2 | -1.1 | 0.7 | -0.7 | 0 | |
| -1.5 | -0.8375 | 0.35 | -0.7 | 0 | |
| -1 | -0.75 | 0 | -0.7 | 0 | Hochpunkt H(-1|-0.75) |
| -0.5 | -0.8375 | -0.35 | -0.7 | 0 | |
| 0 | -1.1 | -0.7 | -0.7 | 0 | Schnittpunkt Sy(0|-1.1) |
| 0.5 | -1.5375 | -1.05 | -0.7 | 0 | |
| 1 | -2.15 | -1.4 | -0.7 | 0 | |
| 1.5 | -2.9375 | -1.75 | -0.7 | 0 | |
| 2 | -3.9 | -2.1 | -0.7 | 0 | |
| 2.5 | -5.0375 | -2.45 | -0.7 | 0 | |
| 3 | -6.35 | -2.8 | -0.7 | 0 | |
| 3.5 | -7.8375 | -3.15 | -0.7 | 0 | |
| 4 | -9.5 | -3.5 | -0.7 | 0 | |
| 4.5 | -11.3375 | -3.85 | -0.7 | 0 | |
| 5 | -13.35 | -4.2 | -0.7 | 0 | |
| 5.5 | -15.5375 | -4.55 | -0.7 | 0 | |
| 6 | -17.9 | -4.9 | -0.7 | 0 | |
| 6.5 | -20.4375 | -5.25 | -0.7 | 0 | |
| 7 | -23.15 | -5.6 | -0.7 | 0 | |
| 7.5 | -26.0375 | -5.95 | -0.7 | 0 | |
| 8 | -29.1 | -6.3 | -0.7 | 0 | |
| 8.5 | -32.3375 | -6.65 | -0.7 | 0 | |
| 9 | -35.75 | -7 | -0.7 | 0 | |
| 9.5 | -39.3375 | -7.35 | -0.7 | 0 | |
| 10 | -43.1 | -7.7 | -0.7 | 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