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Funktion: f(x) = x4, Df = R, Wf = [0; +∞), Potenzfunktion 4. Grades, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | 160000 | -32000 | 4800 | -479.99 | |
-19.5 | 144590.0625 | -29659.5 | 4563 | -467.99 | |
-19 | 130321 | -27436 | 4332 | -455.99 | |
-18.5 | 117135.0625 | -25326.5 | 4107 | -443.98 | |
-18 | 104976 | -23328 | 3888 | -431.98 | |
-17.5 | 93789.0625 | -21437.5 | 3675 | -419.99 | |
-17 | 83521 | -19652 | 3468 | -407.99 | |
-16.5 | 74120.0625 | -17968.5 | 3267 | -395.98 | |
-16 | 65536 | -16384 | 3072 | -383.98 | |
-15.5 | 57720.0625 | -14895.5 | 2883 | -371.98 | |
-15 | 50625 | -13500 | 2700 | -359.98 | |
-14.5 | 44205.0625 | -12194.5 | 2523 | -347.98 | |
-14 | 38416 | -10976 | 2352 | -335.98 | |
-13.5 | 33215.0625 | -9841.5 | 2187 | -323.98 | |
-13 | 28561 | -8788 | 2028 | -311.98 | |
-12.5 | 24414.0625 | -7812.5 | 1875 | -299.98 | |
-12 | 20736 | -6912 | 1728 | -287.98 | |
-11.5 | 17490.0625 | -6083.5 | 1587 | -275.98 | |
-11 | 14641 | -5324 | 1452 | -263.98 | |
-10.5 | 12155.0625 | -4630.5 | 1323 | -251.97 | |
-10 | 10000 | -4000 | 1200 | -239.98 | |
-9.5 | 8145.0625 | -3429.5 | 1083 | -227.98 | |
-9 | 6561 | -2916 | 972 | -215.98 | |
-8.5 | 5220.0625 | -2456.5 | 867 | -203.98 | |
-8 | 4096 | -2048 | 768 | -191.98 | |
-7.5 | 3164.0625 | -1687.5 | 675 | -179.98 | |
-7 | 2401 | -1372 | 588 | -167.98 | |
-6.5 | 1785.0625 | -1098.5 | 507 | -155.98 | |
-6 | 1296 | -864 | 432 | -143.98 | |
-5.5 | 915.0625 | -665.5 | 363 | -131.98 | |
-5 | 625 | -500 | 300 | -119.98 | |
-4.5 | 410.0625 | -364.5 | 243 | -107.98 | |
-4 | 256 | -256 | 192 | -95.98 | |
-3.5 | 150.0625 | -171.5 | 147 | -83.98 | |
-3 | 81 | -108 | 108 | -71.98 | |
-2.5 | 39.0625 | -62.5 | 75 | -59.98 | |
-2 | 16 | -32 | 48 | -47.98 | |
-1.5 | 5.0625 | -13.5 | 27 | -35.98 | |
-1 | 1 | -4 | 12 | -23.98 | |
-0.5 | 0.0625 | -0.5 | 3 | -11.98 | |
0 | 0 | 0 | 0 | 0.02 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
0.5 | 0.0625 | 0.5 | 3 | 12.02 | |
1 | 1 | 4 | 12 | 24.02 | |
1.5 | 5.0625 | 13.5 | 27 | 36.02 | |
2 | 16 | 32 | 48 | 48.02 | |
2.5 | 39.0625 | 62.5 | 75 | 60.02 | |
3 | 81 | 108 | 108 | 72.02 | |
3.5 | 150.0625 | 171.5 | 147 | 84.02 | |
4 | 256 | 256 | 192 | 96.02 | |
4.5 | 410.0625 | 364.5 | 243 | 108.02 | |
5 | 625 | 500 | 300 | 120.02 | |
5.5 | 915.0625 | 665.5 | 363 | 132.02 | |
6 | 1296 | 864 | 432 | 144.02 | |
6.5 | 1785.0625 | 1098.5 | 507 | 156.02 | |
7 | 2401 | 1372 | 588 | 168.02 | |
7.5 | 3164.0625 | 1687.5 | 675 | 180.02 | |
8 | 4096 | 2048 | 768 | 192.02 | |
8.5 | 5220.0625 | 2456.5 | 867 | 204.02 | |
9 | 6561 | 2916 | 972 | 216.02 | |
9.5 | 8145.0625 | 3429.5 | 1083 | 228.02 | |
10 | 10000 | 4000 | 1200 | 240.02 | |
10.5 | 12155.0625 | 4630.5 | 1323 | 252.02 | |
11 | 14641 | 5324 | 1452 | 264.02 | |
11.5 | 17490.0625 | 6083.5 | 1587 | 276.02 | |
12 | 20736 | 6912 | 1728 | 288.02 | |
12.5 | 24414.0625 | 7812.5 | 1875 | 300.02 | |
13 | 28561 | 8788 | 2028 | 312.02 | |
13.5 | 33215.0625 | 9841.5 | 2187 | 324.02 | |
14 | 38416 | 10976 | 2352 | 336.02 | |
14.5 | 44205.0625 | 12194.5 | 2523 | 348.02 | |
15 | 50625 | 13500 | 2700 | 360.02 | |
15.5 | 57720.0625 | 14895.5 | 2883 | 372.02 | |
16 | 65536 | 16384 | 3072 | 384.03 | |
16.5 | 74120.0625 | 17968.5 | 3267 | 396.03 | |
17 | 83521 | 19652 | 3468 | 408.03 | |
17.5 | 93789.0625 | 21437.5 | 3675 | 420.03 | |
18 | 104976 | 23328 | 3888 | 432.03 | |
18.5 | 117135.0625 | 25326.5 | 4107 | 444.04 | |
19 | 130321 | 27436 | 4332 | 456.04 | |
19.5 | 144590.0625 | 29659.5 | 4563 | 468.03 | |
20 | 160000 | 32000 | 4800 | 480.03 | |
Graph: | |||||
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