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Funktion: f(x) = x3(x+6)2/50, 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 | -320 | 256 | -155.2 | 66.7 | |
| -9.5 | -210.0569 | 186.37 | -124.07 | 57.88 | |
| -9 | -131.22 | 131.22 | -97.2 | 49.66 | |
| -8.5 | -76.7656 | 88.51 | -74.29 | 42.05 | |
| -8 | -40.96 | 56.32 | -55.04 | 35.03 | |
| -7.5 | -18.9844 | 32.91 | -39.15 | 28.61 | |
| -7 | -6.86 | 16.66 | -26.32 | 22.79 | |
| -6.5 | -1.3731 | 6.13 | -16.25 | 17.57 | |
| -6 | 0 | 0 | -8.64 | 12.95 | Nullstelle N(-6|0) = Hochpunkt H(-6|0) |
| -5.5 | -0.8319 | -2.87 | -3.19 | 8.93 | |
| -5.07 | -2.2543 | -3.51 | 0 | 5.96 | Wendepunkt W(-5.07|-2.25) |
| -5 | -2.5 | -3.5 | 0.4 | 5.51 | |
| -4.5 | -4.1006 | -2.73 | 2.43 | 2.69 | |
| -4 | -5.12 | -1.28 | 3.2 | 0.48 | |
| -3.6 | -5.3748 | 0 | 3.11 | -0.87 | Tiefpunkt T(-3.6|-5.37) |
| -3.5 | -5.3594 | 0.31 | 3.01 | -1.14 | |
| -3 | -4.86 | 1.62 | 2.16 | -2.16 | |
| -2.5 | -3.8281 | 2.41 | 0.95 | -2.58 | |
| -2.132 | -2.8998 | 2.58 | 0 | -2.51 | Wendepunkt W(-2.13|-2.9) |
| -2 | -2.56 | 2.56 | -0.32 | -2.4 | |
| -1.5 | -1.3669 | 2.13 | -1.35 | -1.62 | |
| -1 | -0.5 | 1.3 | -1.84 | -0.24 | |
| -0.5 | -0.0756 | 0.43 | -1.49 | 1.74 | |
| 0 | 0 | 0 | 0 | 4.33 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) = Sattelpunkt WS(0|0) |
| 0.5 | 0.1056 | 0.67 | 2.93 | 7.51 | |
| 1 | 0.98 | 3.22 | 7.6 | 11.29 | |
| 1.5 | 3.7969 | 8.61 | 14.31 | 15.67 | |
| 2 | 10.24 | 17.92 | 23.36 | 20.65 | |
| 2.5 | 22.5781 | 32.41 | 35.05 | 26.23 | |
| 3 | 43.74 | 53.46 | 49.68 | 32.41 | |
| 3.5 | 77.3894 | 82.63 | 67.55 | 39.19 | |
| 4 | 128 | 121.6 | 88.96 | 46.58 | |
| 4.5 | 200.9306 | 172.23 | 114.21 | 54.56 | |
| 5 | 302.5 | 236.5 | 143.6 | 63.14 | |
| 5.5 | 440.0619 | 316.57 | 177.43 | 72.32 | |
| 6 | 622.08 | 414.72 | 216 | 82.1 | |
| 6.5 | 858.2031 | 533.41 | 259.61 | 92.48 | |
| 7 | 1159.34 | 675.22 | 308.56 | 103.46 | |
| 7.5 | 1537.7344 | 842.91 | 363.15 | 115.04 | |
| 8 | 2007.04 | 1039.36 | 423.68 | 127.22 | |
| 8.5 | 2582.3956 | 1267.63 | 490.45 | 140.01 | |
| 9 | 3280.5 | 1530.9 | 563.76 | 153.39 | |
| 9.5 | 4119.6869 | 1832.53 | 643.91 | 167.37 | |
| 10 | 5120 | 2176 | 731.2 | 181.95 | |
| 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