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Funktion: f(x) = -(x+2)5/40, Df = R, Wf = R, Potenzfunktion 5. Grades, entlang der x-Achse nach links verschoben, Funktion punktsymmetrisch zum Punkt W(-2|0), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 47239.2 | -13122 | 2916 | -485.95 | |
| -19.5 | 41032.7148 | -11723.63 | 2679.69 | -459.33 | |
| -19 | 35496.425 | -10440.13 | 2456.5 | -433.46 | |
| -18.5 | 30574.5258 | -9265.01 | 2246.06 | -408.33 | |
| -18 | 26214.4 | -8192 | 2048 | -383.96 | |
| -17.5 | 22366.5242 | -7215.01 | 1861.94 | -360.33 | |
| -17 | 18984.375 | -6328.13 | 1687.5 | -337.46 | |
| -16.5 | 16024.3352 | -5525.63 | 1524.31 | -315.33 | |
| -16 | 13445.6 | -4802 | 1372 | -293.96 | |
| -15.5 | 11210.0836 | -4151.88 | 1230.19 | -273.34 | |
| -15 | 9282.325 | -3570.13 | 1098.5 | -253.46 | |
| -14.5 | 7629.3945 | -3051.76 | 976.56 | -234.34 | |
| -14 | 6220.8 | -2592 | 864 | -215.96 | |
| -13.5 | 5028.393 | -2186.26 | 760.44 | -198.34 | |
| -13 | 4026.275 | -1830.13 | 665.5 | -181.47 | |
| -12.5 | 3190.7039 | -1519.38 | 578.81 | -165.34 | |
| -12 | 2500 | -1250 | 500 | -149.97 | |
| -11.5 | 1934.4523 | -1018.13 | 428.69 | -135.35 | |
| -11 | 1476.225 | -820.13 | 364.5 | -121.47 | |
| -10.5 | 1109.2633 | -652.51 | 307.06 | -108.35 | |
| -10 | 819.2 | -512 | 256 | -95.98 | |
| -9.5 | 593.2617 | -395.51 | 210.94 | -84.35 | |
| -9 | 420.175 | -300.13 | 171.5 | -73.48 | |
| -8.5 | 290.0727 | -223.13 | 137.31 | -63.36 | |
| -8 | 194.4 | -162 | 108 | -53.98 | |
| -7.5 | 125.8211 | -114.38 | 83.19 | -45.36 | |
| -7 | 78.125 | -78.13 | 62.5 | -37.49 | |
| -6.5 | 46.132 | -51.26 | 45.56 | -30.36 | |
| -6 | 25.6 | -32 | 32 | -23.99 | |
| -5.5 | 13.1305 | -18.76 | 21.44 | -18.36 | |
| -5 | 6.075 | -10.13 | 13.5 | -13.49 | |
| -4.5 | 2.4414 | -4.88 | 7.81 | -9.37 | |
| -4 | 0.8 | -2 | 4 | -5.99 | |
| -3.5 | 0.1898 | -0.63 | 1.69 | -3.37 | |
| -3 | 0.025 | -0.13 | 0.5 | -1.5 | |
| -2.5 | 0.0008 | -0.01 | 0.06 | -0.37 | |
| -2 | 0 | 0 | 0 | 0 | Nullstelle N(-2|0) = Wendepunkt W(-2|0) = Sattelpunkt WS(-2|0) |
| -1.5 | -0.0008 | -0.01 | -0.06 | -0.38 | |
| -1 | -0.025 | -0.13 | -0.5 | -1.5 | |
| -0.5 | -0.1898 | -0.63 | -1.69 | -3.38 | |
| 0 | -0.8 | -2 | -4 | -6.01 | Schnittpunkt Sy(0|-0.8) |
| 0.5 | -2.4414 | -4.88 | -7.81 | -9.38 | |
| 1 | -6.075 | -10.13 | -13.5 | -13.51 | |
| 1.5 | -13.1305 | -18.76 | -21.44 | -18.39 | |
| 2 | -25.6 | -32 | -32 | -24.01 | |
| 2.5 | -46.132 | -51.26 | -45.56 | -30.39 | |
| 3 | -78.125 | -78.13 | -62.5 | -37.51 | |
| 3.5 | -125.8211 | -114.38 | -83.19 | -45.39 | |
| 4 | -194.4 | -162 | -108 | -54.02 | |
| 4.5 | -290.0727 | -223.13 | -137.31 | -63.39 | |
| 5 | -420.175 | -300.13 | -171.5 | -73.52 | |
| 5.5 | -593.2617 | -395.51 | -210.94 | -84.4 | |
| 6 | -819.2 | -512 | -256 | -96.02 | |
| 6.5 | -1109.2633 | -652.51 | -307.06 | -108.4 | |
| 7 | -1476.225 | -820.13 | -364.5 | -121.53 | |
| 7.5 | -1934.4523 | -1018.13 | -428.69 | -135.4 | |
| 8 | -2500 | -1250 | -500 | -150.03 | |
| 8.5 | -3190.7039 | -1519.38 | -578.81 | -165.41 | |
| 9 | -4026.275 | -1830.13 | -665.5 | -181.53 | |
| 9.5 | -5028.393 | -2186.26 | -760.44 | -198.41 | |
| 10 | -6220.8 | -2592 | -864 | -216.04 | |
| 10.5 | -7629.3945 | -3051.76 | -976.56 | -234.41 | |
| 11 | -9282.325 | -3570.13 | -1098.5 | -253.54 | |
| 11.5 | -11210.0836 | -4151.88 | -1230.19 | -273.41 | |
| 12 | -13445.6 | -4802 | -1372 | -294.04 | |
| 12.5 | -16024.3352 | -5525.63 | -1524.31 | -315.42 | |
| 13 | -18984.375 | -6328.13 | -1687.5 | -337.54 | |
| 13.5 | -22366.5242 | -7215.01 | -1861.94 | -360.42 | |
| 14 | -26214.4 | -8192 | -2048 | -384.04 | |
| 14.5 | -30574.5258 | -9265.01 | -2246.06 | -408.41 | |
| 15 | -35496.425 | -10440.13 | -2456.5 | -433.54 | |
| 15.5 | -41032.7148 | -11723.63 | -2679.69 | -459.41 | |
| 16 | -47239.2 | -13122 | -2916 | -486.06 | |
| 16.5 | -54174.9664 | -14641.88 | -3165.81 | -513.44 | |
| 17 | -61902.475 | -16290.13 | -3429.5 | -541.56 | |
| 17.5 | -70487.6555 | -18073.76 | -3707.44 | -570.44 | |
| 18 | -80000 | -20000 | -4000 | -600.07 | |
| 18.5 | -90512.657 | -22076.26 | -4307.56 | -630.44 | |
| 19 | -102102.525 | -24310.13 | -4630.5 | -661.57 | |
| 19.5 | -114850.3461 | -26709.38 | -4969.19 | -693.46 | |
| 20 | -128840.8 | -29282 | -5324 | -726.08 | |
| 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