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Funktion: f(x) = -0.25·x4 + x3 - 6x2, Df = R, Wf = (-∞; 0], Polynom 4. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -4100 | 1420 | -372 | 65.97 | |
| -9.5 | -3435.1406 | 1242.13 | -339.75 | 62.97 | |
| -9 | -2855.25 | 1080 | -309 | 59.97 | |
| -8.5 | -2352.6406 | 932.88 | -279.75 | 56.97 | |
| -8 | -1920 | 800 | -252 | 53.97 | |
| -7.5 | -1550.3906 | 680.63 | -225.75 | 50.97 | |
| -7 | -1237.25 | 574 | -201 | 47.97 | |
| -6.5 | -974.3906 | 479.38 | -177.75 | 44.97 | |
| -6 | -756 | 396 | -156 | 41.97 | |
| -5.5 | -576.6406 | 323.13 | -135.75 | 38.97 | |
| -5 | -431.25 | 260 | -117 | 35.97 | |
| -4.5 | -315.1406 | 205.88 | -99.75 | 32.97 | |
| -4 | -224 | 160 | -84 | 29.97 | |
| -3.5 | -153.8906 | 121.63 | -69.75 | 26.97 | |
| -3 | -101.25 | 90 | -57 | 23.97 | |
| -2.5 | -62.8906 | 64.38 | -45.75 | 20.97 | |
| -2 | -36 | 44 | -36 | 17.97 | |
| -1.5 | -18.1406 | 28.13 | -27.75 | 14.97 | |
| -1 | -7.25 | 16 | -21 | 11.97 | |
| -0.5 | -1.6406 | 6.88 | -15.75 | 8.97 | |
| 0 | 0 | 0 | -12 | 5.97 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Hochpunkt H(0|0) |
| 0.5 | -1.3906 | -5.37 | -9.75 | 2.97 | |
| 1 | -5.25 | -10 | -9 | -0.03 | |
| 1.5 | -11.3906 | -14.63 | -9.75 | -3.03 | |
| 2 | -20 | -20 | -12 | -6.03 | |
| 2.5 | -31.6406 | -26.88 | -15.75 | -9.03 | |
| 3 | -47.25 | -36 | -21 | -12.03 | |
| 3.5 | -68.1406 | -48.13 | -27.75 | -15.03 | |
| 4 | -96 | -64 | -36 | -18.03 | |
| 4.5 | -132.8906 | -84.38 | -45.75 | -21.03 | |
| 5 | -181.25 | -110 | -57 | -24.03 | |
| 5.5 | -243.8906 | -141.63 | -69.75 | -27.03 | |
| 6 | -324 | -180 | -84 | -30.03 | |
| 6.5 | -425.1406 | -225.88 | -99.75 | -33.03 | |
| 7 | -551.25 | -280 | -117 | -36.03 | |
| 7.5 | -706.6406 | -343.13 | -135.75 | -39.03 | |
| 8 | -896 | -416 | -156 | -42.03 | |
| 8.5 | -1124.3906 | -499.38 | -177.75 | -45.03 | |
| 9 | -1397.25 | -594 | -201 | -48.03 | |
| 9.5 | -1720.3906 | -700.63 | -225.75 | -51.03 | |
| 10 | -2100 | -820 | -252 | -54.03 | |
| 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