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Funktion: f(x) = , Df = R, Wf = R, Wurzelfunktion, Funktion punktsymmetrisch zu O(0|0), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-40 | 0.3394 | -0.03 | 0 | 0 | |
-39.5 | 0.3241 | -0.03 | 0 | 0 | |
-39 | 0.3088 | -0.03 | 0 | 0 | |
-38.5 | 0.2933 | -0.03 | 0 | 0 | |
-38 | 0.2778 | -0.03 | 0 | 0 | |
-37.5 | 0.2621 | -0.03 | 0 | 0 | |
-37 | 0.2464 | -0.03 | 0 | 0 | |
-36.5 | 0.2305 | -0.03 | 0 | 0 | |
-36 | 0.2146 | -0.03 | 0 | 0 | |
-35.5 | 0.1985 | -0.03 | 0 | 0 | |
-35 | 0.1824 | -0.03 | 0 | 0 | |
-34.5 | 0.1661 | -0.03 | 0 | 0 | |
-34 | 0.1497 | -0.03 | 0 | 0 | |
-33.5 | 0.1332 | -0.03 | 0 | 0 | |
-33 | 0.1166 | -0.03 | 0 | 0 | |
-32.5 | 0.0998 | -0.03 | 0 | 0 | |
-32 | 0.083 | -0.03 | 0 | 0 | |
-31.5 | 0.066 | -0.03 | 0 | 0 | |
-31 | 0.0488 | -0.03 | 0 | 0 | |
-30.5 | 0.0316 | -0.03 | 0 | 0 | |
-30 | 0.0142 | -0.03 | 0 | 0 | |
-29.6 | 0 | -0.04 | 0 | 0 | Nullstelle N(-29.6|0) |
-29.5 | -0.0033 | -0.04 | 0 | 0 | |
-29 | -0.0209 | -0.04 | 0 | 0 | |
-28.5 | -0.0387 | -0.04 | 0 | 0 | |
-28 | -0.0567 | -0.04 | 0 | 0 | |
-27.5 | -0.0748 | -0.04 | 0 | 0 | |
-27 | -0.093 | -0.04 | 0 | 0 | |
-26.5 | -0.1114 | -0.04 | 0 | 0 | |
-26 | -0.13 | -0.04 | 0 | 0 | |
-25.5 | -0.1487 | -0.04 | 0 | 0 | |
-25 | -0.1676 | -0.04 | 0 | 0 | |
-24.5 | -0.1867 | -0.04 | 0 | 0 | |
-24 | -0.2059 | -0.04 | 0 | 0 | |
-23.5 | -0.2253 | -0.04 | 0 | 0 | |
-23 | -0.2449 | -0.04 | 0 | 0 | |
-22.5 | -0.2647 | -0.04 | 0 | 0 | |
-22 | -0.2847 | -0.04 | 0 | 0 | |
-21.5 | -0.3049 | -0.04 | 0 | 0 | |
-21 | -0.3254 | -0.04 | 0 | 0 | |
-20.5 | -0.346 | -0.04 | 0 | 0 | |
-20 | -0.3668 | -0.04 | 0 | 0 | |
-19.5 | -0.3879 | -0.04 | 0 | 0 | |
-19 | -0.4092 | -0.04 | 0 | 0 | |
-18.5 | -0.4308 | -0.04 | 0 | 0 | |
-18 | -0.4526 | -0.04 | 0 | 0 | |
-17.5 | -0.4747 | -0.04 | 0 | 0 | |
-17 | -0.497 | -0.04 | 0 | 0 | |
-16.5 | -0.5197 | -0.05 | 0 | 0 | |
-16 | -0.5426 | -0.05 | 0 | 0 | |
-15.5 | -0.5658 | -0.05 | 0 | 0 | |
-15 | -0.5893 | -0.05 | 0 | 0 | |
-14.5 | -0.6132 | -0.05 | 0 | 0 | |
-14 | -0.6374 | -0.05 | 0 | 0 | |
-13.5 | -0.6619 | -0.05 | 0 | 0 | |
-13 | -0.6868 | -0.05 | 0 | 0 | |
-12.5 | -0.7121 | -0.05 | 0 | 0 | |
-12 | -0.7378 | -0.05 | 0 | 0 | |
-11.5 | -0.7639 | -0.05 | 0 | 0 | |
-11 | -0.7905 | -0.05 | 0 | 0 | |
-10.5 | -0.8175 | -0.05 | 0 | 0 | |
-10 | -0.845 | -0.06 | 0 | 0 | |
-9.5 | -0.873 | -0.06 | 0 | 0 | |
-9 | -0.9015 | -0.06 | 0 | 0 | |
-8.5 | -0.9306 | -0.06 | 0 | 0 | |
-8 | -0.9603 | -0.06 | 0 | 0 | |
-7.5 | -0.9906 | -0.06 | 0 | 0 | |
-7 | -1.0216 | -0.06 | 0 | 0 | |
-6.5 | -1.0533 | -0.06 | 0 | 0 | |
-6 | -1.0857 | -0.07 | 0 | 0 | |
-5.5 | -1.1188 | -0.07 | 0 | 0 | |
-5 | -1.1528 | -0.07 | 0 | 0 | |
-4.5 | -1.1876 | -0.07 | 0 | 0 | |
-4 | -1.2233 | -0.07 | 0 | 0 | |
-3.5 | -1.2598 | -0.07 | 0 | 0 | |
-3 | -1.297 | -0.08 | 0 | 0 | |
-2.52 | -1.3332 | -0.08 | 0 | 0.01 | Wendepunkt W(-2.52|-1.33) |
-2.5 | -1.3347 | -0.08 | 0 | 0.01 | |
-2 | -1.3723 | -0.07 | 0.01 | 0.02 | |
-1.5 | -1.4084 | -0.07 | 0.02 | 0.05 | |
-1 | -1.4387 | -0.05 | 0.07 | 0.21 | |
-0.65 | -1.449 | 0 | 0.23 | 0.89 | Tiefpunkt T(-0.65|-1.45) |
-0.5 | -1.4461 | 0.05 | 0.43 | 2.08 | |
0 | 0 | Infinity | Infinity | Infinity | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
0.5 | 1.4461 | 0.05 | -0.43 | 1.95 | |
0.65 | 1.449 | 0 | -0.24 | 0.89 | Hochpunkt H(0.65|1.45) |
1 | 1.4387 | -0.05 | -0.07 | 0.2 | |
1.5 | 1.4084 | -0.07 | -0.02 | 0.05 | |
2 | 1.3723 | -0.07 | -0.01 | 0.02 | |
2.5 | 1.3347 | -0.08 | 0 | 0.01 | |
2.51 | 1.334 | -0.08 | 0 | 0.01 | Wendepunkt W(2.51|1.33) |
3 | 1.297 | -0.08 | 0 | 0 | |
3.5 | 1.2598 | -0.07 | 0 | 0 | |
4 | 1.2233 | -0.07 | 0 | 0 | |
4.5 | 1.1876 | -0.07 | 0 | 0 | |
5 | 1.1528 | -0.07 | 0 | 0 | |
5.5 | 1.1188 | -0.07 | 0 | 0 | |
6 | 1.0857 | -0.07 | 0 | 0 | |
6.5 | 1.0533 | -0.06 | 0 | 0 | |
7 | 1.0216 | -0.06 | 0 | 0 | |
7.5 | 0.9906 | -0.06 | 0 | 0 | |
8 | 0.9603 | -0.06 | 0 | 0 | |
8.5 | 0.9306 | -0.06 | 0 | 0 | |
9 | 0.9015 | -0.06 | 0 | 0 | |
9.5 | 0.873 | -0.06 | 0 | 0 | |
10 | 0.845 | -0.06 | 0 | 0 | |
10.5 | 0.8175 | -0.05 | 0 | 0 | |
11 | 0.7905 | -0.05 | 0 | 0 | |
11.5 | 0.7639 | -0.05 | 0 | 0 | |
12 | 0.7378 | -0.05 | 0 | 0 | |
12.5 | 0.7121 | -0.05 | 0 | 0 | |
13 | 0.6868 | -0.05 | 0 | 0 | |
13.5 | 0.6619 | -0.05 | 0 | 0 | |
14 | 0.6374 | -0.05 | 0 | 0 | |
14.5 | 0.6132 | -0.05 | 0 | 0 | |
15 | 0.5893 | -0.05 | 0 | 0 | |
15.5 | 0.5658 | -0.05 | 0 | 0 | |
16 | 0.5426 | -0.05 | 0 | 0 | |
16.5 | 0.5197 | -0.05 | 0 | 0 | |
17 | 0.497 | -0.04 | 0 | 0 | |
17.5 | 0.4747 | -0.04 | 0 | 0 | |
18 | 0.4526 | -0.04 | 0 | 0 | |
18.5 | 0.4308 | -0.04 | 0 | 0 | |
19 | 0.4092 | -0.04 | 0 | 0 | |
19.5 | 0.3879 | -0.04 | 0 | 0 | |
20 | 0.3668 | -0.04 | 0 | 0 | |
20.5 | 0.346 | -0.04 | 0 | 0 | |
21 | 0.3254 | -0.04 | 0 | 0 | |
21.5 | 0.3049 | -0.04 | 0 | 0 | |
22 | 0.2847 | -0.04 | 0 | 0 | |
22.5 | 0.2647 | -0.04 | 0 | 0 | |
23 | 0.2449 | -0.04 | 0 | 0 | |
23.5 | 0.2253 | -0.04 | 0 | 0 | |
24 | 0.2059 | -0.04 | 0 | 0 | |
24.5 | 0.1867 | -0.04 | 0 | 0 | |
25 | 0.1676 | -0.04 | 0 | 0 | |
25.5 | 0.1487 | -0.04 | 0 | 0 | |
26 | 0.13 | -0.04 | 0 | 0 | |
26.5 | 0.1114 | -0.04 | 0 | 0 | |
27 | 0.093 | -0.04 | 0 | 0 | |
27.5 | 0.0748 | -0.04 | 0 | 0 | |
28 | 0.0567 | -0.04 | 0 | 0 | |
28.5 | 0.0387 | -0.04 | 0 | 0 | |
29 | 0.0209 | -0.04 | 0 | 0 | |
29.5 | 0.0033 | -0.04 | 0 | 0 | |
29.6 | 0 | -0.04 | 0 | 0 | Nullstelle N(29.6|0) |
30 | -0.0142 | -0.03 | 0 | 0 | |
30.5 | -0.0316 | -0.03 | 0 | 0 | |
31 | -0.0488 | -0.03 | 0 | 0 | |
31.5 | -0.066 | -0.03 | 0 | 0 | |
32 | -0.083 | -0.03 | 0 | 0 | |
32.5 | -0.0998 | -0.03 | 0 | 0 | |
33 | -0.1166 | -0.03 | 0 | 0 | |
33.5 | -0.1332 | -0.03 | 0 | 0 | |
34 | -0.1497 | -0.03 | 0 | 0 | |
34.5 | -0.1661 | -0.03 | 0 | 0 | |
35 | -0.1824 | -0.03 | 0 | 0 | |
35.5 | -0.1985 | -0.03 | 0 | 0 | |
36 | -0.2146 | -0.03 | 0 | 0 | |
36.5 | -0.2305 | -0.03 | 0 | 0 | |
37 | -0.2464 | -0.03 | 0 | 0 | |
37.5 | -0.2621 | -0.03 | 0 | 0 | |
38 | -0.2778 | -0.03 | 0 | 0 | |
38.5 | -0.2933 | -0.03 | 0 | 0 | |
39 | -0.3088 | -0.03 | 0 | 0 | |
39.5 | -0.3241 | -0.03 | 0 | 0 | |
40 | -0.3394 | -0.03 | 0 | 0 | |
Graph: | |||||
Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann