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Funktion: f(x) = 0.5·x3(6-x), Df = R, Wf = (-∞; 68.34375], Polynom 4. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -8000 | 2900 | -780 | 138 | |
| -9.5 | -6644.6562 | 2527 | -712.5 | 132 | |
| -9 | -5467.5 | 2187 | -648 | 126 | |
| -8.5 | -4452.4062 | 1878.5 | -586.5 | 120 | |
| -8 | -3584 | 1600 | -528 | 114 | |
| -7.5 | -2847.6562 | 1350 | -472.5 | 108 | |
| -7 | -2229.5 | 1127 | -420 | 102 | |
| -6.5 | -1716.4062 | 929.5 | -370.5 | 96 | |
| -6 | -1296 | 756 | -324 | 89.99 | |
| -5.5 | -956.6562 | 605 | -280.5 | 83.99 | |
| -5 | -687.5 | 475 | -240 | 77.99 | |
| -4.5 | -478.4062 | 364.5 | -202.5 | 71.99 | |
| -4 | -320 | 272 | -168 | 65.99 | |
| -3.5 | -203.6562 | 196 | -136.5 | 59.99 | |
| -3 | -121.5 | 135 | -108 | 53.99 | |
| -2.5 | -66.4062 | 87.5 | -82.5 | 47.99 | |
| -2 | -32 | 52 | -60 | 41.99 | |
| -1.5 | -12.6562 | 27 | -40.5 | 35.99 | |
| -1 | -3.5 | 11 | -24 | 29.99 | |
| -0.5 | -0.4062 | 2.5 | -10.5 | 23.99 | |
| 0 | 0 | 0 | 0 | 17.99 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) = Sattelpunkt WS(0|0) |
| 0.5 | 0.3438 | 2 | 7.5 | 11.99 | |
| 1 | 2.5 | 7 | 12 | 5.99 | |
| 1.5 | 7.5938 | 13.5 | 13.5 | -0.01 | |
| 2 | 16 | 20 | 12 | -6.01 | |
| 2.5 | 27.3438 | 25 | 7.5 | -12.01 | |
| 2.999 | 40.473 | 27 | 0 | -17.99 | Wendepunkt W(3|40.47) |
| 3 | 40.5 | 27 | 0 | -18.01 | |
| 3.5 | 53.5938 | 24.5 | -10.5 | -24.01 | |
| 4 | 64 | 16 | -24 | -30.01 | |
| 4.5 | 68.3438 | 0 | -40.5 | -36.01 | Hochpunkt H(4.5|68.34) |
| 5 | 62.5 | -25 | -60 | -42.01 | |
| 5.5 | 41.5938 | -60.5 | -82.5 | -48.01 | |
| 6 | 0 | -108 | -108 | -54.01 | Nullstelle N(6|0) |
| 6.5 | -68.6562 | -169 | -136.5 | -60.01 | |
| 7 | -171.5 | -245 | -168 | -66.01 | |
| 7.5 | -316.4062 | -337.5 | -202.5 | -72.01 | |
| 8 | -512 | -448 | -240 | -78.01 | |
| 8.5 | -767.6562 | -578 | -280.5 | -84.01 | |
| 9 | -1093.5 | -729 | -324 | -90.01 | |
| 9.5 | -1500.4062 | -902.5 | -370.5 | -96.01 | |
| 10 | -2000 | -1100 | -420 | -102.01 | |
| 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