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Funktion: f(x) = -(x-5)6, Df = R, Wf = (-∞ 0], Potenzfunktion 6. Grades, nach unten geöffnet, entlang der x-Achse nach rechts verschoben, Funktion achsensymmetrisch zur Senkrechten x = 5, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | -244140625 | 58593751.25 | -11718750.07 | 1874804.5 | |
-19.5 | -216270112.5156 | 52964110.36 | -10809001.95 | 1764550.81 | |
-19 | -191102976 | 47775745.11 | -9953280.06 | 1658685.51 | |
-18.5 | -168425239.5156 | 43002189.85 | -9149401.93 | 1557156.44 | |
-18 | -148035889 | 38618058.97 | -8395230.05 | 1459859.31 | |
-17.5 | -129746337.8906 | 34599024.35 | -7688671.93 | 1366704.7 | |
-17 | -113379904 | 30921792.85 | -7027680.05 | 1277595.76 | |
-16.5 | -98771297.6406 | 27564083.86 | -6410251.93 | 1192450.52 | |
-16 | -85766121 | 24504606.74 | -5834430.05 | 1111160.96 | |
-15.5 | -74220378.7656 | 21723038.38 | -5298301.95 | 1033678.65 | |
-15 | -64000000 | 19200000.64 | -4800000.06 | 959863.89 | |
-14.5 | -54980371.2656 | 16917037.91 | -4337701.94 | 889655.2 | |
-14 | -47045881 | 14856594.55 | -3909630.06 | 822957.61 | |
-13.5 | -40089475.1406 | 13001992.44 | -3514051.93 | 759677.96 | |
-13 | -34012224 | 11337408.47 | -3149280.05 | 699728.73 | |
-12.5 | -28722900.3906 | 9847851.99 | -2813671.92 | 643019.56 | |
-12 | -24137569 | 8519142.39 | -2505630.04 | 589459.2 | |
-11.5 | -20179187.0156 | 7337886.55 | -2223601.91 | 538961.03 | |
-11 | -16777216 | 6291456.33 | -1966080.04 | 491432.38 | |
-10.5 | -13867245.0156 | 5367966.11 | -1731601.9 | 446777.33 | |
-10 | -11390625 | 4556250.27 | -1518750.03 | 404917.64 | |
-9.5 | -9294114.3906 | 3845840.68 | -1326151.9 | 365758.31 | |
-9 | -7529536 | 3226944.22 | -1152480.02 | 329209.03 | |
-8.5 | -6053445.1406 | 2690420.26 | -996451.9 | 295178.96 | |
-8 | -4826809 | 2227758.18 | -856830.02 | 263580.12 | |
-7.5 | -3814697.2656 | 1831054.84 | -732421.89 | 234319.13 | |
-7 | -2985984 | 1492992.14 | -622080.02 | 207308.56 | |
-6.5 | -2313060.7656 | 1206814.43 | -524701.89 | 182457.5 | |
-6 | -1771561 | 966306.11 | -439230.01 | 159676.71 | |
-5.5 | -1340095.6406 | 765769.03 | -364651.89 | 138875.45 | |
-5 | -1000000 | 600000.08 | -300000.01 | 119964.18 | |
-4.5 | -735091.8906 | 464268.63 | -244351.89 | 102852.65 | |
-4 | -531441 | 354294.06 | -196830.01 | 87450.9 | |
-3.5 | -377149.5156 | 266223.24 | -156601.88 | 73669.11 | |
-3 | -262144 | 196608.04 | -122880.01 | 61416.98 | |
-2.5 | -177978.5156 | 142382.85 | -94921.88 | 50604.77 | |
-2 | -117649 | 100842.03 | -72030.01 | 41142.38 | |
-1.5 | -75418.8906 | 69617.46 | -53551.88 | 32939.79 | |
-1 | -46656 | 46656.02 | -38880 | 25907.05 | |
-0.5 | -27680.6406 | 30197.08 | -27451.88 | 19954.11 | |
0 | -15625 | 18750.01 | -18750 | 14991 | Schnittpunkt Sy(0|-15625) |
0.5 | -8303.7656 | 11071.69 | -12301.88 | 10927.71 | |
1 | -4096 | 6144.01 | -7680 | 7674.24 | |
1.5 | -1838.2656 | 3151.32 | -4501.88 | 5140.59 | |
2 | -729 | 1458 | -2430 | 3236.76 | |
2.5 | -244.1406 | 585.94 | -1171.88 | 1872.75 | |
3 | -64 | 192 | -480 | 958.56 | |
3.5 | -11.3906 | 45.56 | -151.88 | 404.19 | |
4 | -1 | 6 | -30 | 119.64 | |
4.5 | -0.0156 | 0.19 | -1.88 | 14.91 | |
5 | 0 | 0 | 0 | 0 | Nullstelle N(5|0) = Hochpunkt H(5|0) |
5.5 | -0.0156 | -0.19 | -1.88 | -15.09 | |
6 | -1 | -6 | -30 | -120.36 | |
6.5 | -11.3906 | -45.56 | -151.88 | -405.81 | |
7 | -64 | -192 | -480 | -961.44 | |
7.5 | -244.1406 | -585.94 | -1171.88 | -1877.25 | |
8 | -729 | -1458 | -2430 | -3243.24 | |
8.5 | -1838.2656 | -3151.32 | -4501.88 | -5149.41 | |
9 | -4096 | -6144.01 | -7680 | -7685.76 | |
9.5 | -8303.7656 | -11071.69 | -12301.88 | -10942.29 | |
10 | -15625 | -18750.01 | -18750 | -15009 | |
10.5 | -27680.6406 | -30197.08 | -27451.88 | -19975.89 | |
11 | -46656 | -46656.02 | -38880 | -25932.94 | |
11.5 | -75418.8906 | -69617.46 | -53551.88 | -32970.18 | |
12 | -117649 | -100842.03 | -72030.01 | -41177.6 | |
12.5 | -177978.5156 | -142382.85 | -94921.88 | -50645.2 | |
13 | -262144 | -196608.04 | -122880.01 | -61462.98 | |
13.5 | -377149.5156 | -266223.24 | -156601.88 | -73720.9 | |
14 | -531441 | -354294.06 | -196830.01 | -87508.96 | |
14.5 | -735091.8906 | -464268.63 | -244351.89 | -102917.29 | |
15 | -1000000 | -600000.08 | -300000.01 | -120035.75 | |
15.5 | -1340095.6406 | -765769.03 | -364651.89 | -138954.32 | |
16 | -1771561 | -966306.11 | -439230.01 | -159763.96 | |
16.5 | -2313060.7656 | -1206814.43 | -524701.89 | -182553.19 | |
17 | -2985984 | -1492992.14 | -622080.02 | -207412.52 | |
17.5 | -3814697.2656 | -1831054.84 | -732421.89 | -234432.17 | |
18 | -4826809 | -2227758.18 | -856830.02 | -263701.66 | |
18.5 | -6053445.1406 | -2690420.26 | -996451.9 | -295312.14 | |
19 | -7529536 | -3226944.22 | -1152480.02 | -329351.75 | |
19.5 | -9294114.3906 | -3845840.68 | -1326151.9 | -365912.45 | |
20 | -11390625 | -4556250.27 | -1518750.03 | -405082.94 | |
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