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Funktion: f(x) = x4 - 4x3 + 10x2 - 24, Df = R, Wf = [-24; +∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -5 | 1351 | -900 | 440 | -143.99 | |
| -4.5 | 953.0625 | -697.5 | 371 | -131.99 | |
| -4 | 648 | -528 | 308 | -119.99 | |
| -3.5 | 420.0625 | -388.5 | 251 | -107.99 | |
| -3 | 255 | -276 | 200 | -95.99 | |
| -2.5 | 140.0625 | -187.5 | 155 | -83.99 | |
| -2 | 64 | -120 | 116 | -71.99 | |
| -1.5 | 17.0625 | -70.5 | 83 | -59.99 | |
| -1.213 | 0 | -49.06 | 66.77 | -53.1 | Nullstelle N(-1.21|0) |
| -1 | -9 | -36 | 56 | -47.99 | |
| -0.5 | -20.9375 | -13.5 | 35 | -35.99 | |
| 0 | -24 | 0 | 20 | -23.99 | Schnittpunkt Sy(0|-24) = Tiefpunkt T(0|-24) |
| 0.5 | -21.9375 | 7.5 | 11 | -11.99 | |
| 1 | -17 | 12 | 8 | 0.01 | |
| 1.5 | -9.9375 | 16.5 | 11 | 12.01 | |
| 2 | 0 | 24 | 20 | 24.01 | Nullstelle N(2|0) |
| 2.5 | 15.0625 | 37.5 | 35 | 36.01 | |
| 3 | 39 | 60 | 56 | 48.01 | |
| 3.5 | 77.0625 | 94.5 | 83 | 60.01 | |
| 4 | 136 | 144 | 116 | 72.01 | |
| 4.5 | 224.0625 | 211.5 | 155 | 84.01 | |
| 5 | 351 | 300 | 200 | 96.01 | |
| 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