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Funktion: f(x) = (x-3)5/900 + 12, Df = R, Wf = R, Potenzfunktion 5. Grades, entlang der x-Achse und y-Achse verschoben, Funktion punktsymmetrisch zum Punkt W(3|12), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | -7139.4922 | 1554.67 | -270.38 | 35.26 | |
-19.5 | -6395.2266 | 1423.83 | -253.13 | 33.75 | |
-19 | -5714.2578 | 1301.42 | -236.62 | 32.26 | |
-18.5 | -5092.4598 | 1187.08 | -220.85 | 30.81 | |
-18 | -4525.89 | 1080.45 | -205.8 | 29.4 | |
-17.5 | -4010.7848 | 981.17 | -191.45 | 28.01 | |
-17 | -3543.5556 | 888.89 | -177.78 | 26.66 | |
-16.5 | -3120.7847 | 803.28 | -164.78 | 25.35 | |
-16 | -2739.2211 | 724.01 | -152.42 | 24.06 | |
-15.5 | -2395.7763 | 650.75 | -140.7 | 22.81 | |
-15 | -2087.52 | 583.2 | -129.6 | 21.6 | |
-14.5 | -1811.6762 | 521.05 | -119.1 | 20.41 | |
-14 | -1565.6189 | 464.01 | -109.18 | 19.26 | |
-13.5 | -1346.8678 | 411.78 | -99.83 | 18.15 | |
-13 | -1153.0844 | 364.09 | -91.02 | 17.06 | |
-12.5 | -982.0677 | 320.67 | -82.75 | 16.01 | |
-12 | -831.75 | 281.25 | -75 | 15 | |
-11.5 | -700.1927 | 245.58 | -67.75 | 14.01 | |
-11 | -585.5822 | 213.42 | -60.98 | 13.06 | |
-10.5 | -486.2259 | 184.53 | -54.68 | 12.15 | |
-10 | -400.5478 | 158.67 | -48.82 | 11.26 | |
-9.5 | -327.0842 | 135.63 | -43.4 | 10.41 | |
-9 | -264.48 | 115.2 | -38.4 | 9.6 | |
-8.5 | -211.4841 | 97.17 | -33.8 | 8.82 | |
-8 | -166.9456 | 81.34 | -29.58 | 8.07 | |
-7.5 | -129.8091 | 67.53 | -25.73 | 7.35 | |
-7 | -99.1111 | 55.56 | -22.22 | 6.67 | |
-6.5 | -73.9757 | 45.25 | -19.05 | 6.02 | |
-6 | -53.61 | 36.45 | -16.2 | 5.4 | |
-5.5 | -37.3006 | 29 | -13.65 | 4.82 | |
-5 | -24.4089 | 22.76 | -11.38 | 4.27 | |
-4.5 | -14.3672 | 17.58 | -9.38 | 3.75 | |
-4 | -6.6744 | 13.34 | -7.62 | 3.27 | |
-3.5 | -0.8921 | 9.92 | -6.1 | 2.82 | |
-3.408 | 0 | 9.37 | -5.85 | 2.74 | Nullstelle N(-3.41|0) |
-3 | 3.36 | 7.2 | -4.8 | 2.4 | |
-2.5 | 6.408 | 5.08 | -3.7 | 2.02 | |
-2 | 8.5278 | 3.47 | -2.78 | 1.67 | |
-1.5 | 9.9497 | 2.28 | -2.03 | 1.35 | |
-1 | 10.8622 | 1.42 | -1.42 | 1.07 | |
-0.5 | 11.4164 | 0.83 | -0.95 | 0.82 | |
0 | 11.73 | 0.45 | -0.6 | 0.6 | Schnittpunkt Sy(0|11.73) |
0.5 | 11.8915 | 0.22 | -0.35 | 0.42 | |
1 | 11.9644 | 0.09 | -0.18 | 0.27 | |
1.5 | 11.9916 | 0.03 | -0.08 | 0.15 | |
2 | 11.9989 | 0.01 | -0.02 | 0.07 | |
2.5 | 12 | 0 | 0 | 0.02 | |
3 | 12 | 0 | 0 | 0 | |
3.002 | 12 | 0 | 0 | 0 | Wendepunkt W(3|12) = Sattelpunkt WS(3|12) |
3.5 | 12 | 0 | 0 | 0.02 | |
4 | 12.0011 | 0.01 | 0.02 | 0.07 | |
4.5 | 12.0084 | 0.03 | 0.08 | 0.15 | |
5 | 12.0356 | 0.09 | 0.18 | 0.27 | |
5.5 | 12.1085 | 0.22 | 0.35 | 0.42 | |
6 | 12.27 | 0.45 | 0.6 | 0.6 | |
6.5 | 12.5836 | 0.83 | 0.95 | 0.82 | |
7 | 13.1378 | 1.42 | 1.42 | 1.07 | |
7.5 | 14.0503 | 2.28 | 2.03 | 1.35 | |
8 | 15.4722 | 3.47 | 2.78 | 1.67 | |
8.5 | 17.592 | 5.08 | 3.7 | 2.02 | |
9 | 20.64 | 7.2 | 4.8 | 2.4 | |
9.5 | 24.8921 | 9.92 | 6.1 | 2.82 | |
10 | 30.6744 | 13.34 | 7.62 | 3.27 | |
10.5 | 38.3672 | 17.58 | 9.38 | 3.75 | |
11 | 48.4089 | 22.76 | 11.38 | 4.27 | |
11.5 | 61.3006 | 29 | 13.65 | 4.82 | |
12 | 77.61 | 36.45 | 16.2 | 5.4 | |
12.5 | 97.9757 | 45.25 | 19.05 | 6.02 | |
13 | 123.1111 | 55.56 | 22.22 | 6.67 | |
13.5 | 153.8091 | 67.53 | 25.73 | 7.35 | |
14 | 190.9456 | 81.34 | 29.58 | 8.07 | |
14.5 | 235.4841 | 97.17 | 33.8 | 8.82 | |
15 | 288.48 | 115.2 | 38.4 | 9.6 | |
15.5 | 351.0842 | 135.63 | 43.4 | 10.42 | |
16 | 424.5478 | 158.67 | 48.82 | 11.27 | |
16.5 | 510.2259 | 184.53 | 54.68 | 12.15 | |
17 | 609.5822 | 213.42 | 60.98 | 13.07 | |
17.5 | 724.1927 | 245.58 | 67.75 | 14.02 | |
18 | 855.75 | 281.25 | 75 | 15 | |
18.5 | 1006.0677 | 320.67 | 82.75 | 16.02 | |
19 | 1177.0844 | 364.09 | 91.02 | 17.07 | |
19.5 | 1370.8678 | 411.78 | 99.83 | 18.15 | |
20 | 1589.6189 | 464.01 | 109.18 | 19.27 | |
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