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Funktion: f(x) = -x3 + 2x2 + 7x - 14, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt W(0.67|-8.75), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 8646 | -1273 | 124 | -6 | |
| -19.5 | 8024.875 | -1211.75 | 121 | -6 | |
| -19 | 7434 | -1152 | 118 | -6 | |
| -18.5 | 6872.625 | -1093.75 | 115 | -6 | |
| -18 | 6340 | -1037 | 112 | -6 | |
| -17.5 | 5835.375 | -981.75 | 109 | -6 | |
| -17 | 5358 | -928 | 106 | -6 | |
| -16.5 | 4907.125 | -875.75 | 103 | -6 | |
| -16 | 4482 | -825 | 100 | -6 | |
| -15.5 | 4081.875 | -775.75 | 97 | -6 | |
| -15 | 3706 | -728 | 94 | -6 | |
| -14.5 | 3353.625 | -681.75 | 91 | -6 | |
| -14 | 3024 | -637 | 88 | -6 | |
| -13.5 | 2716.375 | -593.75 | 85 | -6 | |
| -13 | 2430 | -552 | 82 | -6 | |
| -12.5 | 2164.125 | -511.75 | 79 | -6 | |
| -12 | 1918 | -473 | 76 | -6 | |
| -11.5 | 1690.875 | -435.75 | 73 | -6 | |
| -11 | 1482 | -400 | 70 | -6 | |
| -10.5 | 1290.625 | -365.75 | 67 | -6 | |
| -10 | 1116 | -333 | 64 | -6 | |
| -9.5 | 957.375 | -301.75 | 61 | -6 | |
| -9 | 814 | -272 | 58 | -6 | |
| -8.5 | 685.125 | -243.75 | 55 | -6 | |
| -8 | 570 | -217 | 52 | -6 | |
| -7.5 | 467.875 | -191.75 | 49 | -6 | |
| -7 | 378 | -168 | 46 | -6 | |
| -6.5 | 299.625 | -145.75 | 43 | -6 | |
| -6 | 232 | -125 | 40 | -6 | |
| -5.5 | 174.375 | -105.75 | 37 | -6 | |
| -5 | 126 | -88 | 34 | -6 | |
| -4.5 | 86.125 | -71.75 | 31 | -6 | |
| -4 | 54 | -57 | 28 | -6 | |
| -3.5 | 28.875 | -43.75 | 25 | -6 | |
| -3 | 10 | -32 | 22 | -6 | |
| -2.646 | 0.0061 | -24.59 | 19.88 | -6 | Nullstelle N(-2.65|0.01) |
| -2.5 | -3.375 | -21.75 | 19 | -6 | |
| -2 | -12 | -13 | 16 | -6 | |
| -1.5 | -16.625 | -5.75 | 13 | -6 | |
| -1 | -18 | 0 | 10 | -6 | Tiefpunkt T(-1|-18) |
| -0.5 | -16.875 | 4.25 | 7 | -6 | |
| 0 | -14 | 7 | 4 | -6 | Schnittpunkt Sy(0|-14) |
| 0.5 | -10.125 | 8.25 | 1 | -6 | |
| 0.666 | -8.7463 | 8.33 | 0 | -6 | Wendepunkt W(0.67|-8.75) |
| 1 | -6 | 8 | -2 | -6 | |
| 1.5 | -2.375 | 6.25 | -5 | -6 | |
| 2 | 0 | 3 | -8 | -6 | Nullstelle N(2|0) |
| 2.333 | 0.5185 | 0 | -10 | -6 | Hochpunkt H(2.33|0.52) |
| 2.5 | 0.375 | -1.75 | -11 | -6 | |
| 2.645 | 0.0026 | -3.41 | -11.87 | -6 | Nullstelle N(2.65|0) |
| 3 | -2 | -8 | -14 | -6 | |
| 3.5 | -7.875 | -15.75 | -17 | -6 | |
| 4 | -18 | -25 | -20 | -6 | |
| 4.5 | -33.125 | -35.75 | -23 | -6 | |
| 5 | -54 | -48 | -26 | -6 | |
| 5.5 | -81.375 | -61.75 | -29 | -6 | |
| 6 | -116 | -77 | -32 | -6 | |
| 6.5 | -158.625 | -93.75 | -35 | -6 | |
| 7 | -210 | -112 | -38 | -6 | |
| 7.5 | -270.875 | -131.75 | -41 | -6 | |
| 8 | -342 | -153 | -44 | -6 | |
| 8.5 | -424.125 | -175.75 | -47 | -6 | |
| 9 | -518 | -200 | -50 | -6 | |
| 9.5 | -624.375 | -225.75 | -53 | -6 | |
| 10 | -744 | -253 | -56 | -6 | |
| 10.5 | -877.625 | -281.75 | -59 | -6 | |
| 11 | -1026 | -312 | -62 | -6 | |
| 11.5 | -1189.875 | -343.75 | -65 | -6 | |
| 12 | -1370 | -377 | -68 | -6 | |
| 12.5 | -1567.125 | -411.75 | -71 | -6 | |
| 13 | -1782 | -448 | -74 | -6 | |
| 13.5 | -2015.375 | -485.75 | -77 | -6 | |
| 14 | -2268 | -525 | -80 | -6 | |
| 14.5 | -2540.625 | -565.75 | -83 | -6 | |
| 15 | -2834 | -608 | -86 | -6 | |
| 15.5 | -3148.875 | -651.75 | -89 | -6 | |
| 16 | -3486 | -697 | -92 | -6 | |
| 16.5 | -3846.125 | -743.75 | -95 | -6 | |
| 17 | -4230 | -792 | -98 | -6 | |
| 17.5 | -4638.375 | -841.75 | -101 | -6 | |
| 18 | -5072 | -893 | -104 | -6 | |
| 18.5 | -5531.625 | -945.75 | -107 | -6 | |
| 19 | -6018 | -1000 | -110 | -6 | |
| 19.5 | -6531.875 | -1055.75 | -113 | -6 | |
| 20 | -7074 | -1113 | -116 | -6 | |
| 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