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Funktion: f(x) = -1.5·(x+2.5)3, Df = R, Wf = R, Potenzfunktion 3. Grades, gespiegelt an der x-Achse, entlang der x-Achse verschoben, Funktion punktsymmetrisch zum Punkt W(-2.5|0), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 632.8125 | -253.13 | 67.5 | -9 | |
| -9.5 | 514.5 | -220.5 | 63 | -9 | |
| -9 | 411.9375 | -190.13 | 58.5 | -9 | |
| -8.5 | 324 | -162 | 54 | -9 | |
| -8 | 249.5625 | -136.13 | 49.5 | -9 | |
| -7.5 | 187.5 | -112.5 | 45 | -9 | |
| -7 | 136.6875 | -91.13 | 40.5 | -9 | |
| -6.5 | 96 | -72 | 36 | -9 | |
| -6 | 64.3125 | -55.13 | 31.5 | -9 | |
| -5.5 | 40.5 | -40.5 | 27 | -9 | |
| -5 | 23.4375 | -28.13 | 22.5 | -9 | |
| -4.5 | 12 | -18 | 18 | -9 | |
| -4 | 5.0625 | -10.13 | 13.5 | -9 | |
| -3.5 | 1.5 | -4.5 | 9 | -9 | |
| -3 | 0.1875 | -1.13 | 4.5 | -9 | |
| -2.5 | 0 | 0 | 0 | -9 | Nullstelle N(-2.5|0) = Wendepunkt W(-2.5|0) = Sattelpunkt WS(-2.5|0) |
| -2 | -0.1875 | -1.13 | -4.5 | -9 | |
| -1.5 | -1.5 | -4.5 | -9 | -9 | |
| -1 | -5.0625 | -10.13 | -13.5 | -9 | |
| -0.5 | -12 | -18 | -18 | -9 | |
| 0 | -23.4375 | -28.13 | -22.5 | -9 | Schnittpunkt Sy(0|-23.44) |
| 0.5 | -40.5 | -40.5 | -27 | -9 | |
| 1 | -64.3125 | -55.13 | -31.5 | -9 | |
| 1.5 | -96 | -72 | -36 | -9 | |
| 2 | -136.6875 | -91.13 | -40.5 | -9 | |
| 2.5 | -187.5 | -112.5 | -45 | -9 | |
| 3 | -249.5625 | -136.13 | -49.5 | -9 | |
| 3.5 | -324 | -162 | -54 | -9 | |
| 4 | -411.9375 | -190.13 | -58.5 | -9 | |
| 4.5 | -514.5 | -220.5 | -63 | -9 | |
| 5 | -632.8125 | -253.13 | -67.5 | -9 | |
| 5.5 | -768 | -288 | -72 | -9 | |
| 6 | -921.1875 | -325.13 | -76.5 | -9 | |
| 6.5 | -1093.5 | -364.5 | -81 | -9 | |
| 7 | -1286.0625 | -406.13 | -85.5 | -9 | |
| 7.5 | -1500 | -450 | -90 | -9 | |
| 8 | -1736.4375 | -496.13 | -94.5 | -9 | |
| 8.5 | -1996.5 | -544.5 | -99 | -9 | |
| 9 | -2281.3125 | -595.13 | -103.5 | -9 | |
| 9.5 | -2592 | -648 | -108 | -9 | |
| 10 | -2929.6875 | -703.13 | -112.5 | -9 | |
| 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