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Funktion: f(x) = -x4/240 - x3/180 + x2/80 + x + 56, Df = R, Wf = (-∞; 58.81], Polynom 4. Grades, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | -581.2222 | 127.17 | -19.31 | 1.97 | |
| -19.5 | -520.0117 | 117.76 | -18.34 | 1.92 | |
| -19 | -463.3861 | 108.83 | -17.39 | 1.87 | |
| -18.5 | -411.1089 | 100.36 | -16.47 | 1.82 | |
| -18 | -362.95 | 92.35 | -15.58 | 1.77 | |
| -17.5 | -318.6853 | 84.78 | -14.7 | 1.72 | |
| -17 | -278.0972 | 77.64 | -13.86 | 1.67 | |
| -16.5 | -240.9742 | 70.92 | -13.04 | 1.62 | |
| -16 | -207.1111 | 64.6 | -12.24 | 1.57 | |
| -15.5 | -176.3089 | 58.67 | -11.47 | 1.52 | |
| -15 | -148.375 | 53.13 | -10.73 | 1.47 | |
| -14.5 | -123.1228 | 47.94 | -10 | 1.42 | |
| -14 | -100.3722 | 43.12 | -9.31 | 1.37 | |
| -13.5 | -79.9492 | 38.63 | -8.64 | 1.32 | |
| -13 | -61.6861 | 34.48 | -7.99 | 1.27 | |
| -12.5 | -45.4214 | 30.64 | -7.37 | 1.22 | |
| -12 | -31 | 27.1 | -6.78 | 1.17 | |
| -11.5 | -18.2728 | 23.86 | -6.2 | 1.12 | |
| -11 | -7.0972 | 20.89 | -5.66 | 1.07 | |
| -10.644 | 0 | 18.94 | -5.28 | 1.03 | Nullstelle N(-10.64|0) |
| -10.5 | 2.6633 | 18.19 | -5.14 | 1.02 | |
| -10 | 11.1389 | 15.75 | -4.64 | 0.97 | |
| -9.5 | 18.4536 | 13.55 | -4.17 | 0.92 | |
| -9 | 24.725 | 11.58 | -3.73 | 0.87 | |
| -8.5 | 30.0647 | 9.82 | -3.3 | 0.82 | |
| -8 | 34.5778 | 8.27 | -2.91 | 0.77 | |
| -7.5 | 38.3633 | 6.91 | -2.54 | 0.72 | |
| -7 | 41.5139 | 5.73 | -2.19 | 0.67 | |
| -6.5 | 44.1161 | 4.71 | -1.87 | 0.62 | |
| -6 | 46.25 | 3.85 | -1.58 | 0.57 | |
| -5.5 | 47.9897 | 3.13 | -1.3 | 0.52 | |
| -5 | 49.4028 | 2.54 | -1.06 | 0.47 | |
| -4.5 | 50.5508 | 2.07 | -0.84 | 0.42 | |
| -4 | 51.4889 | 1.7 | -0.64 | 0.37 | |
| -3.5 | 52.2661 | 1.42 | -0.47 | 0.32 | |
| -3 | 52.925 | 1.23 | -0.33 | 0.27 | |
| -2.5 | 53.5022 | 1.09 | -0.2 | 0.22 | |
| -2 | 54.0278 | 1.02 | -0.11 | 0.17 | |
| -1.5 | 54.5258 | 0.98 | -0.04 | 0.12 | |
| -1.116 | 54.9008 | 0.97 | 0 | 0.08 | Wendepunkt W(-1.12|54.9) |
| -1 | 55.0139 | 0.98 | 0.01 | 0.07 | |
| -0.5 | 55.5036 | 0.99 | 0.03 | 0.02 | |
| 0 | 56 | 1 | 0.02 | -0.03 | Schnittpunkt Sy(0|56) |
| 0.448 | 56.4498 | 1.01 | 0 | -0.08 | Wendepunkt W(0.45|56.45) |
| 0.5 | 56.5022 | 1.01 | 0 | -0.08 | |
| 1 | 57.0028 | 0.99 | -0.06 | -0.13 | |
| 1.5 | 57.4883 | 0.94 | -0.14 | -0.18 | |
| 2 | 57.9389 | 0.85 | -0.24 | -0.23 | |
| 2.5 | 58.3286 | 0.7 | -0.37 | -0.28 | |
| 3 | 58.625 | 0.47 | -0.53 | -0.33 | |
| 3.5 | 58.7897 | 0.17 | -0.7 | -0.38 | |
| 3.724 | 58.8091 | 0 | -0.79 | -0.41 | Hochpunkt H(3.72|58.81) |
| 4 | 58.7778 | -0.23 | -0.91 | -0.43 | |
| 4.5 | 58.5383 | -0.74 | -1.14 | -0.48 | |
| 5 | 58.0139 | -1.38 | -1.39 | -0.53 | |
| 5.5 | 57.1411 | -2.14 | -1.67 | -0.58 | |
| 6 | 55.85 | -3.05 | -1.98 | -0.63 | |
| 6.5 | 54.0647 | -4.12 | -2.3 | -0.68 | |
| 7 | 51.7028 | -5.36 | -2.66 | -0.73 | |
| 7.5 | 48.6758 | -6.78 | -3.04 | -0.78 | |
| 8 | 44.8889 | -8.4 | -3.44 | -0.83 | |
| 8.5 | 40.2411 | -10.23 | -3.87 | -0.88 | |
| 9 | 34.625 | -12.28 | -4.33 | -0.93 | |
| 9.5 | 27.9272 | -14.56 | -4.8 | -0.98 | |
| 10 | 20.0278 | -17.08 | -5.31 | -1.03 | |
| 10.5 | 10.8008 | -19.87 | -5.84 | -1.08 | |
| 11 | 0.1139 | -22.93 | -6.39 | -1.13 | |
| 11.004 | 0 | -22.95 | -6.4 | -1.13 | Nullstelle N(11|0) |
| 11.5 | -12.1714 | -26.26 | -6.97 | -1.18 | |
| 12 | -26.2 | -29.9 | -7.58 | -1.23 | |
| 12.5 | -42.1228 | -33.84 | -8.2 | -1.28 | |
| 13 | -60.0972 | -38.11 | -8.86 | -1.33 | |
| 13.5 | -80.2867 | -42.71 | -9.54 | -1.38 | |
| 14 | -102.8611 | -47.65 | -10.24 | -1.43 | |
| 14.5 | -127.9964 | -52.95 | -10.97 | -1.48 | |
| 15 | -155.875 | -58.63 | -11.73 | -1.53 | |
| 15.5 | -186.6853 | -64.68 | -12.5 | -1.58 | |
| 16 | -220.6222 | -71.13 | -13.31 | -1.63 | |
| 16.5 | -257.8867 | -77.99 | -14.14 | -1.68 | |
| 17 | -298.6861 | -85.28 | -14.99 | -1.73 | |
| 17.5 | -343.2339 | -92.99 | -15.87 | -1.78 | |
| 18 | -391.75 | -101.15 | -16.78 | -1.83 | |
| 18.5 | -444.4603 | -109.77 | -17.7 | -1.88 | |
| 19 | -501.5972 | -118.86 | -18.66 | -1.93 | |
| 19.5 | -563.3992 | -128.43 | -19.64 | -1.98 | |
| 20 | -630.1111 | -138.5 | -20.64 | -2.03 | |
| 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