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Funktion: f(x) = (x+1)4 - 8, Df = R, Wf = [-8; +∞), Potenzfunktion 4. Grades, nach oben geöffnet, entlang der x-Achse und y-Achse verschoben, Funktion achsensymmetrisch zur Senkrechten x = -1, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 65152.5 | -13718 | 2166 | -227.99 | |
| -19.5 | 58559.5313 | -12663.25 | 2053.5 | -221.99 | |
| -19 | 52480 | -11664 | 1944 | -215.99 | |
| -18.5 | 46886.5313 | -10718.75 | 1837.5 | -210 | |
| -18 | 41752.5 | -9826 | 1734 | -203.99 | |
| -17.5 | 37052.0313 | -8984.25 | 1633.5 | -197.99 | |
| -17 | 32760 | -8192 | 1536 | -191.99 | |
| -16.5 | 28852.0313 | -7447.75 | 1441.5 | -185.99 | |
| -16 | 25304.5 | -6750 | 1350 | -179.99 | |
| -15.5 | 22094.5313 | -6097.25 | 1261.5 | -173.99 | |
| -15 | 19200 | -5488 | 1176 | -167.99 | |
| -14.5 | 16599.5313 | -4920.75 | 1093.5 | -161.99 | |
| -14 | 14272.5 | -4394 | 1014 | -155.99 | |
| -13.5 | 12199.0313 | -3906.25 | 937.5 | -149.99 | |
| -13 | 10360 | -3456 | 864 | -143.99 | |
| -12.5 | 8737.0313 | -3041.75 | 793.5 | -137.99 | |
| -12 | 7312.5 | -2662 | 726 | -131.99 | |
| -11.5 | 6069.5313 | -2315.25 | 661.5 | -125.99 | |
| -11 | 4992 | -2000 | 600 | -119.99 | |
| -10.5 | 4064.5313 | -1714.75 | 541.5 | -113.99 | |
| -10 | 3272.5 | -1458 | 486 | -107.99 | |
| -9.5 | 2602.0313 | -1228.25 | 433.5 | -101.99 | |
| -9 | 2040 | -1024 | 384 | -95.99 | |
| -8.5 | 1574.0313 | -843.75 | 337.5 | -89.99 | |
| -8 | 1192.5 | -686 | 294 | -83.99 | |
| -7.5 | 884.5313 | -549.25 | 253.5 | -77.99 | |
| -7 | 640 | -432 | 216 | -71.99 | |
| -6.5 | 449.5313 | -332.75 | 181.5 | -65.99 | |
| -6 | 304.5 | -250 | 150 | -59.99 | |
| -5.5 | 197.0313 | -182.25 | 121.5 | -53.99 | |
| -5 | 120 | -128 | 96 | -47.99 | |
| -4.5 | 67.0313 | -85.75 | 73.5 | -41.99 | |
| -4 | 32.5 | -54 | 54 | -35.99 | |
| -3.5 | 11.5313 | -31.25 | 37.5 | -29.99 | |
| -3 | 0 | -16 | 24 | -23.99 | Nullstelle N(-3|0) |
| -2.5 | -5.4687 | -6.75 | 13.5 | -17.99 | |
| -2 | -7.5 | -2 | 6 | -11.99 | |
| -1.5 | -7.9687 | -0.25 | 1.5 | -5.99 | |
| -1 | -8 | 0 | 0 | 0.01 | Tiefpunkt T(-1|-8) |
| -0.5 | -7.9687 | 0.25 | 1.5 | 6.01 | |
| 0 | -7.5 | 2 | 6 | 12.01 | Schnittpunkt Sy(0|-7.5) |
| 0.5 | -5.4687 | 6.75 | 13.5 | 18.01 | |
| 1 | 0 | 16 | 24 | 24.01 | Nullstelle N(1|0) |
| 1.5 | 11.5313 | 31.25 | 37.5 | 30.01 | |
| 2 | 32.5 | 54 | 54 | 36.01 | |
| 2.5 | 67.0313 | 85.75 | 73.5 | 42.01 | |
| 3 | 120 | 128 | 96 | 48.01 | |
| 3.5 | 197.0313 | 182.25 | 121.5 | 54.01 | |
| 4 | 304.5 | 250 | 150 | 60.01 | |
| 4.5 | 449.5313 | 332.75 | 181.5 | 66.01 | |
| 5 | 640 | 432 | 216 | 72.01 | |
| 5.5 | 884.5313 | 549.25 | 253.5 | 78.01 | |
| 6 | 1192.5 | 686 | 294 | 84.01 | |
| 6.5 | 1574.0313 | 843.75 | 337.5 | 90.01 | |
| 7 | 2040 | 1024 | 384 | 96.01 | |
| 7.5 | 2602.0313 | 1228.25 | 433.5 | 102.01 | |
| 8 | 3272.5 | 1458 | 486 | 108.01 | |
| 8.5 | 4064.5313 | 1714.75 | 541.5 | 114.01 | |
| 9 | 4992 | 2000 | 600 | 120.01 | |
| 9.5 | 6069.5313 | 2315.25 | 661.5 | 126.01 | |
| 10 | 7312.5 | 2662 | 726 | 132.01 | |
| 10.5 | 8737.0313 | 3041.75 | 793.5 | 138.01 | |
| 11 | 10360 | 3456 | 864 | 144.01 | |
| 11.5 | 12199.0313 | 3906.25 | 937.5 | 150.01 | |
| 12 | 14272.5 | 4394 | 1014 | 156.01 | |
| 12.5 | 16599.5313 | 4920.75 | 1093.5 | 162.01 | |
| 13 | 19200 | 5488 | 1176 | 168.01 | |
| 13.5 | 22094.5313 | 6097.25 | 1261.5 | 174.01 | |
| 14 | 25304.5 | 6750 | 1350 | 180.01 | |
| 14.5 | 28852.0313 | 7447.75 | 1441.5 | 186.01 | |
| 15 | 32760 | 8192 | 1536 | 192 | |
| 15.5 | 37052.0313 | 8984.25 | 1633.5 | 198 | |
| 16 | 41752.5 | 9826 | 1734 | 204.01 | |
| 16.5 | 46886.5313 | 10718.75 | 1837.5 | 210.02 | |
| 17 | 52480 | 11664 | 1944 | 216.02 | |
| 17.5 | 58559.5313 | 12663.25 | 2053.5 | 222.02 | |
| 18 | 65152.5 | 13718 | 2166 | 228.02 | |
| 18.5 | 72287.0313 | 14829.75 | 2281.5 | 234.02 | |
| 19 | 79992 | 16000 | 2400 | 240.02 | |
| 19.5 | 88297.0313 | 17230.25 | 2521.5 | 246.02 | |
| 20 | 97232.5 | 18522 | 2646 | 252.02 | |
| 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