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Funktion: f(x) = x5 - 4x4 + 2x - 4, Df = R, Wf = R, Polynom 5. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -140024 | 66002 | -24800 | 6958.69 | |
| -9.5 | -109981.3437 | 54445.32 | -21479.5 | 6325.75 | |
| -9 | -85315 | 44471 | -18468 | 5722.81 | |
| -8.5 | -65271.7812 | 35928.32 | -15750.5 | 5149.88 | |
| -8 | -49172 | 28674 | -13312 | 4606.95 | |
| -7.5 | -36405.7187 | 22572.32 | -11137.5 | 4094 | |
| -7 | -26429 | 17495 | -9212 | 3611.07 | |
| -6.5 | -18760.1562 | 13321.31 | -7520.5 | 3158.12 | |
| -6 | -12976 | 9938 | -6048 | 2735.18 | |
| -5.5 | -8708.0937 | 7239.31 | -4779.5 | 2342.24 | |
| -5 | -5639 | 5127 | -3700 | 1979.3 | |
| -4.5 | -3498.5312 | 3510.31 | -2794.5 | 1646.36 | |
| -4 | -2060 | 2306 | -2048 | 1343.42 | |
| -3.5 | -1136.4687 | 1438.31 | -1445.5 | 1070.48 | |
| -3 | -577 | 839 | -972 | 827.54 | |
| -2.5 | -262.9062 | 447.31 | -612.5 | 614.6 | |
| -2 | -104 | 210 | -352 | 431.66 | |
| -1.5 | -34.8437 | 81.31 | -175.5 | 278.72 | |
| -1 | -11 | 23 | -68 | 155.78 | |
| -0.5 | -5.2812 | 4.31 | -14.5 | 62.84 | |
| 0 | -4 | 2 | 0 | -0.1 | Schnittpunkt Sy(0|-4) |
| 0.5 | -3.2187 | 0.31 | -9.5 | -33.04 | |
| 0.53 | -3.2138 | 0 | -10.51 | -34.06 | Hochpunkt H(0.53|-3.21) |
| 1 | -5 | -9 | -28 | -35.98 | |
| 1.5 | -13.6562 | -26.69 | -40.5 | -8.92 | |
| 2 | -32 | -46 | -32 | 48.14 | |
| 2.398 | -52.1776 | -53.3 | 0 | 115.01 | Wendepunkt W(2.4|-52.18) |
| 2.5 | -57.5937 | -52.69 | 12.5 | 135.2 | |
| 3 | -79 | -25 | 108 | 252.26 | |
| 3.186 | -81.4982 | 0 | 159.57 | 303.47 | Tiefpunkt T(3.19|-81.5) |
| 3.5 | -72.0312 | 66.31 | 269.5 | 399.32 | |
| 3.984 | 0 | 249.88 | 502.83 | 570.25 | Nullstelle N(3.98|0) |
| 4 | 4 | 258 | 512 | 576.38 | |
| 4.5 | 210.0313 | 594.31 | 850.5 | 783.44 | |
| 5 | 631 | 1127 | 1300 | 1020.5 | |
| 5.5 | 1379.5938 | 1915.31 | 1875.5 | 1287.56 | |
| 6 | 2600 | 3026 | 2592 | 1584.62 | |
| 6.5 | 4471.6563 | 4533.31 | 3464.5 | 1911.68 | |
| 7 | 7213 | 6519 | 4508 | 2268.74 | |
| 7.5 | 11085.2188 | 9072.31 | 5737.5 | 2655.8 | |
| 8 | 16396 | 12290 | 7168 | 3072.86 | |
| 8.5 | 23503.2813 | 16276.31 | 8814.5 | 3519.92 | |
| 9 | 32819 | 21143 | 10692 | 3996.98 | |
| 9.5 | 44812.8438 | 27009.32 | 12815.5 | 4504.04 | |
| 10 | 60016 | 34002 | 15200 | 5041.1 | |
| 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