www.michael-buhlmann.de
Funktion: f(x) = x5, Df = R, Wf = R, Potenzfunktion 5. Grades, Funktion punktsymmetrisch zum Punkt O(0|0), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | -3200000 | 800000.02 | -160000 | 23997.74 | |
-19.5 | -2819506.2187 | 722950.33 | -148297.5 | 22813.1 | |
-19 | -2476099 | 651605.01 | -137180 | 21658.02 | |
-18.5 | -2166998.6562 | 585675.33 | -126632.5 | 20532.99 | |
-18 | -1889568 | 524880.01 | -116640 | 19438.1 | |
-17.5 | -1641308.5937 | 468945.32 | -107187.5 | 18373.13 | |
-17 | -1419857 | 417605.01 | -98260 | 17338.26 | |
-16.5 | -1222981.0312 | 370600.32 | -89842.5 | 16333.19 | |
-16 | -1048576 | 327680.01 | -81920 | 15358.18 | |
-15.5 | -894660.9687 | 288600.32 | -74477.5 | 14413.26 | |
-15 | -759375 | 253125.01 | -67500 | 13498.3 | |
-14.5 | -640973.4062 | 221025.32 | -60972.5 | 12613.34 | |
-14 | -537824 | 192080.01 | -54880 | 11758.38 | |
-13.5 | -448403.3437 | 166075.32 | -49207.5 | 10933.45 | |
-13 | -371293 | 142805.01 | -43940 | 10138.49 | |
-12.5 | -305175.7812 | 122070.32 | -39062.5 | 9373.56 | |
-12 | -248832 | 103680.01 | -34560 | 8638.6 | |
-11.5 | -201135.7187 | 87450.32 | -30417.5 | 7933.66 | |
-11 | -161051 | 73205 | -26620 | 7258.71 | |
-10.5 | -127628.1562 | 60775.32 | -23152.5 | 6613.73 | |
-10 | -100000 | 50000 | -20000 | 5998.79 | |
-9.5 | -77378.0937 | 40725.32 | -17147.5 | 5413.85 | |
-9 | -59049 | 32805 | -14580 | 4858.91 | |
-8.5 | -44370.5312 | 26100.32 | -12282.5 | 4333.98 | |
-8 | -32768 | 20480 | -10240 | 3839.04 | |
-7.5 | -23730.4687 | 15820.31 | -8437.5 | 3374.1 | |
-7 | -16807 | 12005 | -6860 | 2939.16 | |
-6.5 | -11602.9062 | 8925.31 | -5492.5 | 2534.22 | |
-6 | -7776 | 6480 | -4320 | 2159.28 | |
-5.5 | -5032.8437 | 4575.31 | -3327.5 | 1814.34 | |
-5 | -3125 | 3125 | -2500 | 1499.4 | |
-4.5 | -1845.2812 | 2050.31 | -1822.5 | 1214.46 | |
-4 | -1024 | 1280 | -1280 | 959.52 | |
-3.5 | -525.2187 | 750.31 | -857.5 | 734.58 | |
-3 | -243 | 405 | -540 | 539.64 | |
-2.5 | -97.6562 | 195.31 | -312.5 | 374.7 | |
-2 | -32 | 80 | -160 | 239.76 | |
-1.5 | -7.5937 | 25.31 | -67.5 | 134.82 | |
-1 | -1 | 5 | -20 | 59.88 | |
-0.5 | -0.0312 | 0.31 | -2.5 | 14.94 | |
0 | 0 | 0 | 0 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
0.5 | 0.0313 | 0.31 | 2.5 | 15.06 | |
1 | 1 | 5 | 20 | 60.12 | |
1.5 | 7.5938 | 25.31 | 67.5 | 135.18 | |
2 | 32 | 80 | 160 | 240.24 | |
2.5 | 97.6563 | 195.31 | 312.5 | 375.3 | |
3 | 243 | 405 | 540 | 540.36 | |
3.5 | 525.2188 | 750.31 | 857.5 | 735.42 | |
4 | 1024 | 1280 | 1280 | 960.48 | |
4.5 | 1845.2813 | 2050.31 | 1822.5 | 1215.54 | |
5 | 3125 | 3125 | 2500 | 1500.6 | |
5.5 | 5032.8438 | 4575.31 | 3327.5 | 1815.66 | |
6 | 7776 | 6480 | 4320 | 2160.72 | |
6.5 | 11602.9063 | 8925.31 | 5492.5 | 2535.78 | |
7 | 16807 | 12005 | 6860 | 2940.84 | |
7.5 | 23730.4688 | 15820.31 | 8437.5 | 3375.9 | |
8 | 32768 | 20480 | 10240 | 3840.95 | |
8.5 | 44370.5313 | 26100.32 | 12282.5 | 4336.01 | |
9 | 59049 | 32805 | 14580 | 4861.08 | |
9.5 | 77378.0938 | 40725.32 | 17147.5 | 5416.13 | |
10 | 100000 | 50000 | 20000 | 6001.19 | |
10.5 | 127628.1563 | 60775.32 | 23152.5 | 6616.25 | |
11 | 161051 | 73205 | 26620 | 7261.3 | |
11.5 | 201135.7188 | 87450.32 | 30417.5 | 7936.35 | |
12 | 248832 | 103680.01 | 34560 | 8641.39 | |
12.5 | 305175.7813 | 122070.32 | 39062.5 | 9376.44 | |
13 | 371293 | 142805.01 | 43940 | 10141.51 | |
13.5 | 448403.3438 | 166075.32 | 49207.5 | 10936.54 | |
14 | 537824 | 192080.01 | 54880 | 11761.61 | |
14.5 | 640973.4063 | 221025.32 | 60972.5 | 12616.66 | |
15 | 759375 | 253125.01 | 67500 | 13501.67 | |
15.5 | 894660.9688 | 288600.32 | 74477.5 | 14416.73 | |
16 | 1048576 | 327680.01 | 81920 | 15362.11 | |
16.5 | 1222981.0313 | 370600.32 | 89842.5 | 16337.09 | |
17 | 1419857 | 417605.01 | 98260 | 17342.1 | |
17.5 | 1641308.5938 | 468945.32 | 107187.5 | 18377.26 | |
18 | 1889568 | 524880.01 | 116640 | 19442.35 | |
18.5 | 2166998.6563 | 585675.33 | 126632.5 | 20537.53 | |
19 | 2476099 | 651605.01 | 137180 | 21662.56 | |
19.5 | 2819506.2188 | 722950.33 | 148297.5 | 22817.52 | |
20 | 3200000 | 800000.02 | 160000 | 24002.86 | |
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