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Funktion: f(x) = -0.004·(x+2.5)6 + 16, Df = R, Wf = (-∞; 16], Potenzfunktion 6. Grades, nach unten geöffnet, entlang der x-Achse und der y-Achse verschoben, Funktion achsensymmetrisch zur Senkrechten x = -2.5, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | -114875.6016 | 39391.41 | -11254.69 | 2572.08 | |
| -19.5 | -96534.276 | 34076.57 | -10022.52 | 2357.84 | |
| -19 | -80700.7481 | 29351.55 | -8894.41 | 2155.84 | |
| -18.5 | -67092.864 | 25165.83 | -7864.32 | 1965.73 | |
| -18 | -55452.9801 | 21471.86 | -6926.41 | 1787.12 | |
| -17.5 | -45546.5 | 18225 | -6075 | 1619.68 | |
| -17 | -37160.4576 | 15383.36 | -5304.61 | 1463.04 | |
| -16.5 | -30102.144 | 12907.78 | -4609.92 | 1316.84 | |
| -16 | -24197.7806 | 10761.68 | -3985.81 | 1180.72 | |
| -15.5 | -19291.236 | 8911.03 | -3427.32 | 1054.32 | |
| -15 | -15242.7891 | 7324.22 | -2929.69 | 937.28 | |
| -14.5 | -11927.936 | 5971.97 | -2488.32 | 829.24 | |
| -14 | -9236.2431 | 4827.26 | -2098.81 | 729.83 | |
| -13.5 | -7070.244 | 3865.22 | -1756.92 | 638.71 | |
| -13 | -5344.3826 | 3063.08 | -1458.61 | 555.5 | |
| -12.5 | -3984 | 2400 | -1200 | 479.86 | |
| -12 | -2924.3676 | 1857.07 | -977.41 | 411.41 | |
| -11.5 | -2109.764 | 1417.18 | -787.32 | 349.8 | |
| -11 | -1492.5981 | 1064.89 | -626.41 | 294.68 | |
| -10.5 | -1032.576 | 786.43 | -491.52 | 245.67 | |
| -10 | -695.9141 | 569.53 | -379.69 | 202.42 | |
| -9.5 | -454.596 | 403.37 | -288.12 | 164.57 | |
| -9 | -285.6756 | 278.47 | -214.21 | 131.76 | |
| -8.5 | -170.624 | 186.62 | -155.52 | 103.63 | |
| -8 | -94.7226 | 120.79 | -109.81 | 79.82 | |
| -7.5 | -46.5 | 75 | -75 | 59.96 | |
| -7 | -17.2151 | 44.29 | -49.21 | 43.71 | |
| -6.5 | -0.384 | 24.58 | -30.72 | 30.7 | |
| -6.486 | 0 | 24.15 | -30.29 | 30.38 | Nullstelle N(-6.49|0) |
| -6 | 8.6469 | 12.61 | -18.01 | 20.56 | |
| -5.5 | 13.084 | 5.83 | -9.72 | 12.95 | |
| -5 | 15.0234 | 2.34 | -4.69 | 7.49 | |
| -4.5 | 15.744 | 0.77 | -1.92 | 3.83 | |
| -4 | 15.9544 | 0.18 | -0.61 | 1.62 | |
| -3.5 | 15.996 | 0.02 | -0.12 | 0.48 | |
| -3 | 15.9999 | 0 | -0.01 | 0.06 | |
| -2.5 | 16 | 0 | 0 | 0 | Hochpunkt W(-2.5|16) |
| -2 | 15.9999 | 0 | -0.01 | -0.06 | |
| -1.5 | 15.996 | -0.02 | -0.12 | -0.48 | |
| -1 | 15.9544 | -0.18 | -0.61 | -1.62 | |
| -0.5 | 15.744 | -0.77 | -1.92 | -3.85 | |
| 0 | 15.0234 | -2.34 | -4.69 | -7.51 | Schnittpunkt Sy(0|15.02) |
| 0.5 | 13.084 | -5.83 | -9.72 | -12.97 | |
| 1 | 8.6469 | -12.61 | -18.01 | -20.6 | |
| 1.484 | 0 | -24.09 | -30.23 | -30.38 | Nullstelle N(1.48|0) |
| 1.5 | -0.384 | -24.58 | -30.72 | -30.74 | |
| 2 | -17.2151 | -44.29 | -49.21 | -43.77 | |
| 2.5 | -46.5 | -75 | -75 | -60.04 | |
| 3 | -94.7226 | -120.79 | -109.81 | -79.9 | |
| 3.5 | -170.624 | -186.62 | -155.52 | -103.73 | |
| 4 | -285.6756 | -278.47 | -214.21 | -131.88 | |
| 4.5 | -454.596 | -403.37 | -288.12 | -164.71 | |
| 5 | -695.9141 | -569.53 | -379.69 | -202.58 | |
| 5.5 | -1032.576 | -786.43 | -491.52 | -245.85 | |
| 6 | -1492.5981 | -1064.89 | -626.41 | -294.88 | |
| 6.5 | -2109.764 | -1417.18 | -787.32 | -350.04 | |
| 7 | -2924.3676 | -1857.07 | -977.41 | -411.67 | |
| 7.5 | -3984 | -2400 | -1200 | -480.15 | |
| 8 | -5344.3826 | -3063.08 | -1458.61 | -555.82 | |
| 8.5 | -7070.244 | -3865.22 | -1756.92 | -639.05 | |
| 9 | -9236.2431 | -4827.26 | -2098.81 | -730.21 | |
| 9.5 | -11927.936 | -5971.97 | -2488.32 | -829.65 | |
| 10 | -15242.7891 | -7324.22 | -2929.69 | -937.72 | |
| 10.5 | -19291.236 | -8911.03 | -3427.32 | -1054.8 | |
| 11 | -24197.7806 | -10761.68 | -3985.81 | -1181.24 | |
| 11.5 | -30102.144 | -12907.78 | -4609.92 | -1317.39 | |
| 12 | -37160.4576 | -15383.36 | -5304.61 | -1463.64 | |
| 12.5 | -45546.5 | -18225 | -6075 | -1620.32 | |
| 13 | -55452.9801 | -21471.86 | -6926.41 | -1787.8 | |
| 13.5 | -67092.864 | -25165.83 | -7864.32 | -1966.41 | |
| 14 | -80700.7481 | -29351.55 | -8894.41 | -2156.57 | |
| 14.5 | -96534.276 | -34076.57 | -10022.52 | -2358.61 | |
| 15 | -114875.6016 | -39391.41 | -11254.69 | -2572.89 | |
| 15.5 | -136032.896 | -45349.63 | -12597.12 | -2799.77 | |
| 16 | -160341.9006 | -52007.97 | -14056.21 | -3039.69 | |
| 16.5 | -188167.524 | -59426.38 | -15638.52 | -3292.87 | |
| 17 | -219905.4851 | -67668.15 | -17350.81 | -3559.72 | |
| 17.5 | -255984 | -76800 | -19200 | -3840.6 | |
| 18 | -296865.5151 | -86892.15 | -21193.21 | -4135.9 | |
| 18.5 | -343048.484 | -98018.43 | -23337.72 | -4445.96 | |
| 19 | -395069.1906 | -110256.34 | -25641.01 | -4771.15 | |
| 19.5 | -453503.616 | -123687.17 | -28110.72 | -5111.8 | |
| 20 | -518969.3516 | -138396.1 | -30754.69 | -5468.26 | |
| 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