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Funktion: f(x) = -x4/2 + 8x3/3, Df = R, Wf = (-∞; 128/3], Polynom 4. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -7666.6667 | 2800 | -760 | 136 | |
| -9.5 | -6358.8646 | 2436.75 | -693.5 | 130 | |
| -9 | -5224.5 | 2106 | -630 | 124 | |
| -8.5 | -4247.6979 | 1806.25 | -569.5 | 118 | |
| -8 | -3413.3333 | 1536 | -512 | 112 | |
| -7.5 | -2707.0312 | 1293.75 | -457.5 | 106 | |
| -7 | -2115.1667 | 1078 | -406 | 100 | |
| -6.5 | -1624.8646 | 887.25 | -357.5 | 93.99 | |
| -6 | -1224 | 720 | -312 | 87.99 | |
| -5.5 | -901.1979 | 574.75 | -269.5 | 81.99 | |
| -5 | -645.8333 | 450 | -230 | 75.99 | |
| -4.5 | -448.0312 | 344.25 | -193.5 | 69.99 | |
| -4 | -298.6667 | 256 | -160 | 63.99 | |
| -3.5 | -189.3646 | 183.75 | -129.5 | 57.99 | |
| -3 | -112.5 | 126 | -102 | 51.99 | |
| -2.5 | -61.1979 | 81.25 | -77.5 | 45.99 | |
| -2 | -29.3333 | 48 | -56 | 39.99 | |
| -1.5 | -11.5312 | 24.75 | -37.5 | 33.99 | |
| -1 | -3.1667 | 10 | -22 | 27.99 | |
| -0.5 | -0.3646 | 2.25 | -9.5 | 21.99 | |
| 0 | 0 | 0 | 0 | 15.99 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) = Sattelpunkt WS(0|0) |
| 0.5 | 0.3021 | 1.75 | 6.5 | 9.99 | |
| 1 | 2.1667 | 6 | 10 | 3.99 | |
| 1.5 | 6.4688 | 11.25 | 10.5 | -2.01 | |
| 2 | 13.3333 | 16 | 8 | -8.01 | |
| 2.5 | 22.1354 | 18.75 | 2.5 | -14.01 | |
| 2.666 | 25.2713 | 18.96 | 0.01 | -16 | Wendepunkt W(2.67|25.27) |
| 3 | 31.5 | 18 | -6 | -20.01 | |
| 3.5 | 39.3021 | 12.25 | -17.5 | -26.01 | |
| 3.999 | 42.6667 | 0 | -31.97 | -31.99 | Hochpunkt H(4|42.67) |
| 4 | 42.6667 | 0 | -32 | -32.01 | |
| 4.5 | 37.9688 | -20.25 | -49.5 | -38.01 | |
| 5 | 20.8333 | -50 | -70 | -44.01 | |
| 5.333 | 0 | -75.82 | -85.32 | -48 | Nullstelle N(5.33|0) |
| 5.5 | -13.8646 | -90.75 | -93.5 | -50.01 | |
| 6 | -72 | -144 | -120 | -56.01 | |
| 6.5 | -160.1979 | -211.25 | -149.5 | -62.01 | |
| 7 | -285.8333 | -294 | -182 | -68.01 | |
| 7.5 | -457.0312 | -393.75 | -217.5 | -74 | |
| 8 | -682.6667 | -512 | -256 | -80.01 | |
| 8.5 | -972.3646 | -650.25 | -297.5 | -86.01 | |
| 9 | -1336.5 | -810 | -342 | -92.01 | |
| 9.5 | -1786.1979 | -992.75 | -389.5 | -98.01 | |
| 10 | -2333.3333 | -1200 | -440 | -104.01 | |
| 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