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Funktion: f(x) = -x5/24, Df = R, Wf = R, Potenzfunktion 5. Grades, entlang der y-Achse nach oben verschoben, Funktion punktsymmetrisch zum Punkt O(0|9), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 133342.3333 | -33333.33 | 6666.67 | -999.91 | |
| -19.5 | 117488.4258 | -30122.93 | 6179.06 | -950.55 | |
| -19 | 103179.7917 | -27150.21 | 5715.83 | -902.41 | |
| -18.5 | 90300.6107 | -24403.14 | 5276.35 | -855.54 | |
| -18 | 78741 | -21870 | 4860 | -809.92 | |
| -17.5 | 68396.8581 | -19539.39 | 4466.15 | -765.54 | |
| -17 | 59169.7083 | -17400.21 | 4094.17 | -722.43 | |
| -16.5 | 50966.543 | -15441.68 | 3743.44 | -680.55 | |
| -16 | 43699.6667 | -13653.33 | 3413.33 | -639.93 | |
| -15.5 | 37286.5404 | -12025.01 | 3103.23 | -600.55 | |
| -15 | 31649.625 | -10546.88 | 2812.5 | -562.43 | |
| -14.5 | 26716.2253 | -9209.39 | 2540.52 | -525.56 | |
| -14 | 22418.3333 | -8003.33 | 2286.67 | -489.93 | |
| -13.5 | 18692.4727 | -6919.8 | 2050.31 | -455.56 | |
| -13 | 15479.5417 | -5950.21 | 1830.83 | -422.44 | |
| -12.5 | 12724.6576 | -5086.26 | 1627.6 | -390.56 | |
| -12 | 10377 | -4320 | 1440 | -359.94 | |
| -11.5 | 8389.6549 | -3643.76 | 1267.4 | -330.57 | |
| -11 | 6719.4583 | -3050.21 | 1109.17 | -302.45 | |
| -10.5 | 5326.8398 | -2532.3 | 964.69 | -275.57 | |
| -10 | 4175.6667 | -2083.33 | 833.33 | -249.95 | |
| -9.5 | 3233.0872 | -1696.89 | 714.48 | -225.58 | |
| -9 | 2469.375 | -1366.88 | 607.5 | -202.45 | |
| -8.5 | 1857.7721 | -1087.51 | 511.77 | -180.58 | |
| -8 | 1374.3333 | -853.33 | 426.67 | -159.96 | |
| -7.5 | 997.7695 | -659.18 | 351.56 | -140.59 | |
| -7 | 709.2917 | -500.21 | 285.83 | -122.47 | |
| -6.5 | 492.4544 | -371.89 | 228.85 | -105.59 | |
| -6 | 333 | -270 | 180 | -89.97 | |
| -5.5 | 218.7018 | -190.64 | 138.65 | -75.6 | |
| -5 | 139.2083 | -130.21 | 104.17 | -62.48 | |
| -4.5 | 85.8867 | -85.43 | 75.94 | -50.6 | |
| -4 | 51.6667 | -53.33 | 53.33 | -39.98 | |
| -3.5 | 30.8841 | -31.26 | 35.73 | -30.61 | |
| -3 | 19.125 | -16.88 | 22.5 | -22.49 | |
| -2.5 | 13.069 | -8.14 | 13.02 | -15.61 | |
| -2 | 10.3333 | -3.33 | 6.67 | -9.99 | |
| -1.5 | 9.3164 | -1.05 | 2.81 | -5.62 | |
| -1 | 9.0417 | -0.21 | 0.83 | -2.5 | |
| -0.5 | 9.0013 | -0.01 | 0.1 | -0.62 | |
| 0 | 9 | 0 | 0 | 0 | Schnittpunkt Sy(0|9) = Wendepunkt W(0|9) = Sattelpunkt WS(0|9) |
| 0.5 | 8.9987 | -0.01 | -0.1 | -0.63 | |
| 1 | 8.9583 | -0.21 | -0.83 | -2.51 | |
| 1.5 | 8.6836 | -1.05 | -2.81 | -5.63 | |
| 2 | 7.6667 | -3.33 | -6.67 | -10.01 | |
| 2.5 | 4.931 | -8.14 | -13.02 | -15.64 | |
| 2.93 | 0 | -15.35 | -20.96 | -21.48 | Nullstelle N(2.93|0) |
| 3 | -1.125 | -16.88 | -22.5 | -22.52 | |
| 3.5 | -12.8841 | -31.26 | -35.73 | -30.64 | |
| 4 | -33.6667 | -53.33 | -53.33 | -40.02 | |
| 4.5 | -67.8867 | -85.43 | -75.94 | -50.65 | |
| 5 | -121.2083 | -130.21 | -104.17 | -62.53 | |
| 5.5 | -200.7018 | -190.64 | -138.65 | -75.65 | |
| 6 | -315 | -270 | -180 | -90.03 | |
| 6.5 | -474.4544 | -371.89 | -228.85 | -105.66 | |
| 7 | -691.2917 | -500.21 | -285.83 | -122.54 | |
| 7.5 | -979.7695 | -659.18 | -351.56 | -140.66 | |
| 8 | -1356.3333 | -853.33 | -426.67 | -160.04 | |
| 8.5 | -1839.7721 | -1087.51 | -511.77 | -180.67 | |
| 9 | -2451.375 | -1366.88 | -607.5 | -202.54 | |
| 9.5 | -3215.0872 | -1696.89 | -714.48 | -225.67 | |
| 10 | -4157.6667 | -2083.33 | -833.33 | -250.05 | |
| 10.5 | -5308.8398 | -2532.3 | -964.69 | -275.68 | |
| 11 | -6701.4583 | -3050.21 | -1109.17 | -302.55 | |
| 11.5 | -8371.6549 | -3643.76 | -1267.4 | -330.68 | |
| 12 | -10359 | -4320 | -1440 | -360.06 | |
| 12.5 | -12706.6576 | -5086.26 | -1627.6 | -390.68 | |
| 13 | -15461.5417 | -5950.21 | -1830.83 | -422.56 | |
| 13.5 | -18674.4727 | -6919.8 | -2050.31 | -455.69 | |
| 14 | -22400.3333 | -8003.33 | -2286.67 | -490.07 | |
| 14.5 | -26698.2253 | -9209.39 | -2540.52 | -525.7 | |
| 15 | -31631.625 | -10546.88 | -2812.5 | -562.57 | |
| 15.5 | -37268.5404 | -12025.01 | -3103.23 | -600.7 | |
| 16 | -43681.6667 | -13653.33 | -3413.33 | -640.09 | |
| 16.5 | -50948.543 | -15441.68 | -3743.44 | -680.71 | |
| 17 | -59151.7083 | -17400.21 | -4094.17 | -722.59 | |
| 17.5 | -68378.8581 | -19539.39 | -4466.15 | -765.72 | |
| 18 | -78723 | -21870 | -4860 | -810.1 | |
| 18.5 | -90282.6107 | -24403.14 | -5276.35 | -855.73 | |
| 19 | -103161.7917 | -27150.21 | -5715.83 | -902.61 | |
| 19.5 | -117470.4258 | -30122.93 | -6179.06 | -950.73 | |
| 20 | -133324.3333 | -33333.33 | -6666.67 | -1000.12 | |
| 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