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Funktion: f(x) = (x-4)4 - 3, Df = R, Wf = [-3; +∞), Potenzfunktion 4. Grades, nach oben geöffnet, entlang der x-Achse und y-Achse verschoben, Funktion achsensymmetrisch zur Senkrechten x = 4, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 331773 | -55296 | 6912 | -576.01 | |
| -19.5 | 304977.0625 | -51911.5 | 6627 | -564 | |
| -19 | 279838 | -48668 | 6348 | -551.97 | |
| -18.5 | 256286.0625 | -45562.5 | 6075 | -540 | |
| -18 | 234253 | -42592 | 5808 | -528 | |
| -17.5 | 213672.0625 | -39753.5 | 5547 | -515.99 | |
| -17 | 194478 | -37044 | 5292 | -503.98 | |
| -16.5 | 176607.0625 | -34460.5 | 5043 | -491.99 | |
| -16 | 159997 | -32000 | 4800 | -479.97 | |
| -15.5 | 144587.0625 | -29659.5 | 4563 | -467.99 | |
| -15 | 130318 | -27436 | 4332 | -455.98 | |
| -14.5 | 117132.0625 | -25326.5 | 4107 | -443.99 | |
| -14 | 104973 | -23328 | 3888 | -431.99 | |
| -13.5 | 93786.0625 | -21437.5 | 3675 | -419.99 | |
| -13 | 83518 | -19652 | 3468 | -407.99 | |
| -12.5 | 74117.0625 | -17968.5 | 3267 | -395.98 | |
| -12 | 65533 | -16384 | 3072 | -383.99 | |
| -11.5 | 57717.0625 | -14895.5 | 2883 | -371.98 | |
| -11 | 50622 | -13500 | 2700 | -359.98 | |
| -10.5 | 44202.0625 | -12194.5 | 2523 | -347.97 | |
| -10 | 38413 | -10976 | 2352 | -335.98 | |
| -9.5 | 33212.0625 | -9841.5 | 2187 | -323.97 | |
| -9 | 28558 | -8788 | 2028 | -311.97 | |
| -8.5 | 24411.0625 | -7812.5 | 1875 | -299.97 | |
| -8 | 20733 | -6912 | 1728 | -287.98 | |
| -7.5 | 17487.0625 | -6083.5 | 1587 | -275.98 | |
| -7 | 14638 | -5324 | 1452 | -263.98 | |
| -6.5 | 12152.0625 | -4630.5 | 1323 | -251.98 | |
| -6 | 9997 | -4000 | 1200 | -239.98 | |
| -5.5 | 8142.0625 | -3429.5 | 1083 | -227.98 | |
| -5 | 6558 | -2916 | 972 | -215.98 | |
| -4.5 | 5217.0625 | -2456.5 | 867 | -203.98 | |
| -4 | 4093 | -2048 | 768 | -191.98 | |
| -3.5 | 3161.0625 | -1687.5 | 675 | -179.98 | |
| -3 | 2398 | -1372 | 588 | -167.98 | |
| -2.5 | 1782.0625 | -1098.5 | 507 | -155.98 | |
| -2 | 1293 | -864 | 432 | -143.98 | |
| -1.5 | 912.0625 | -665.5 | 363 | -131.98 | |
| -1 | 622 | -500 | 300 | -119.98 | |
| -0.5 | 407.0625 | -364.5 | 243 | -107.98 | |
| 0 | 253 | -256 | 192 | -95.98 | Schnittpunkt Sy(0|253) |
| 0.5 | 147.0625 | -171.5 | 147 | -83.98 | |
| 1 | 78 | -108 | 108 | -71.98 | |
| 1.5 | 36.0625 | -62.5 | 75 | -59.98 | |
| 2 | 13 | -32 | 48 | -47.98 | |
| 2.5 | 2.0625 | -13.5 | 27 | -35.98 | |
| 2.682 | 0 | -9.16 | 20.85 | -31.61 | Nullstelle N(2.68|0.02) |
| 3 | -2 | -4 | 12 | -23.98 | |
| 3.5 | -2.9375 | -0.5 | 3 | -11.98 | |
| 4 | -3 | 0 | 0 | 0.02 | Tiefpunkt T(4|-3) |
| 4.5 | -2.9375 | 0.5 | 3 | 12.02 | |
| 5 | -2 | 4 | 12 | 24.02 | |
| 5.316 | 0 | 9.12 | 20.78 | 31.61 | Nullstelle N(5.32|0) |
| 5.5 | 2.0625 | 13.5 | 27 | 36.02 | |
| 6 | 13 | 32 | 48 | 48.02 | |
| 6.5 | 36.0625 | 62.5 | 75 | 60.02 | |
| 7 | 78 | 108 | 108 | 72.02 | |
| 7.5 | 147.0625 | 171.5 | 147 | 84.02 | |
| 8 | 253 | 256 | 192 | 96.02 | |
| 8.5 | 407.0625 | 364.5 | 243 | 108.02 | |
| 9 | 622 | 500 | 300 | 120.02 | |
| 9.5 | 912.0625 | 665.5 | 363 | 132.02 | |
| 10 | 1293 | 864 | 432 | 144.02 | |
| 10.5 | 1782.0625 | 1098.5 | 507 | 156.02 | |
| 11 | 2398 | 1372 | 588 | 168.02 | |
| 11.5 | 3161.0625 | 1687.5 | 675 | 180.02 | |
| 12 | 4093 | 2048 | 768 | 192.02 | |
| 12.5 | 5217.0625 | 2456.5 | 867 | 204.02 | |
| 13 | 6558 | 2916 | 972 | 216.02 | |
| 13.5 | 8142.0625 | 3429.5 | 1083 | 228.02 | |
| 14 | 9997 | 4000 | 1200 | 240.02 | |
| 14.5 | 12152.0625 | 4630.5 | 1323 | 252.02 | |
| 15 | 14638 | 5324 | 1452 | 264.02 | |
| 15.5 | 17487.0625 | 6083.5 | 1587 | 276.02 | |
| 16 | 20733 | 6912 | 1728 | 288.03 | |
| 16.5 | 24411.0625 | 7812.5 | 1875 | 300.03 | |
| 17 | 28558 | 8788 | 2028 | 312.03 | |
| 17.5 | 33212.0625 | 9841.5 | 2187 | 324.03 | |
| 18 | 38413 | 10976 | 2352 | 336.03 | |
| 18.5 | 44202.0625 | 12194.5 | 2523 | 348.03 | |
| 19 | 50622 | 13500 | 2700 | 360.03 | |
| 19.5 | 57717.0625 | 14895.5 | 2883 | 372.03 | |
| 20 | 65533 | 16384 | 3072 | 384.03 | |
| 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