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Funktion: f(x) = , Df = R\{0}, Wf = (-∞; 0.2], gebrochen rationale Funktion, x -> -∞: f(x) -> 0 = y als Grenzkurve, x -> +∞: f(x) -> 0 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | -0.1125 | -0.01 | 0 | 0 | |
-19.5 | -0.1157 | -0.01 | 0 | 0 | |
-19 | -0.1191 | -0.01 | 0 | 0 | |
-18.5 | -0.1227 | -0.01 | 0 | 0 | |
-18 | -0.1265 | -0.01 | 0 | 0 | |
-17.5 | -0.1306 | -0.01 | 0 | 0 | |
-17 | -0.1349 | -0.01 | 0 | 0 | |
-16.5 | -0.1396 | -0.01 | 0 | 0 | |
-16 | -0.1445 | -0.01 | 0 | 0 | |
-15.5 | -0.1498 | -0.01 | 0 | 0 | |
-15 | -0.1556 | -0.01 | 0 | 0 | |
-14.5 | -0.1617 | -0.01 | 0 | 0 | |
-14 | -0.1684 | -0.01 | 0 | 0 | |
-13.5 | -0.1756 | -0.02 | 0 | 0 | |
-13 | -0.1834 | -0.02 | 0 | 0 | |
-12.5 | -0.192 | -0.02 | 0 | 0 | |
-12 | -0.2014 | -0.02 | 0 | 0 | |
-11.5 | -0.2117 | -0.02 | 0 | 0 | |
-11 | -0.2231 | -0.02 | -0.01 | 0 | |
-10.5 | -0.2358 | -0.03 | -0.01 | 0 | |
-10 | -0.25 | -0.03 | -0.01 | 0 | |
-9.5 | -0.2659 | -0.03 | -0.01 | 0 | |
-9 | -0.284 | -0.04 | -0.01 | 0 | |
-8.5 | -0.3045 | -0.04 | -0.01 | -0.01 | |
-8 | -0.3281 | -0.05 | -0.02 | -0.01 | |
-7.5 | -0.3556 | -0.06 | -0.02 | -0.01 | |
-7 | -0.3878 | -0.07 | -0.02 | -0.01 | |
-6.5 | -0.426 | -0.08 | -0.03 | -0.02 | |
-6 | -0.4722 | -0.1 | -0.04 | -0.02 | |
-5.5 | -0.5289 | -0.13 | -0.06 | -0.04 | |
-5 | -0.6 | -0.16 | -0.08 | -0.06 | |
-4.5 | -0.6914 | -0.21 | -0.12 | -0.09 | |
-4 | -0.8125 | -0.28 | -0.18 | -0.16 | |
-3.5 | -0.9796 | -0.4 | -0.29 | -0.31 | |
-3 | -1.2222 | -0.59 | -0.52 | -0.64 | |
-2.5 | -1.6 | -0.96 | -1.02 | -1.54 | |
-2 | -2.25 | -1.75 | -2.38 | -4.51 | |
-1.5 | -3.5556 | -3.85 | -7.11 | -18.23 | |
-1 | -7 | -12 | -34 | -132.65 | |
-0.5 | -24 | -88 | -512.01 | -4072.42 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> -∞ |
0.5 | -16 | 72 | -448.01 | 3611.58 | |
1 | -3 | 8 | -26 | 107.45 | |
1.5 | -0.8889 | 2.07 | -4.74 | 13.39 | |
2 | -0.25 | 0.75 | -1.38 | 2.99 | |
2.5 | 0 | 0.32 | -0.51 | 0.92 | Nullstelle N(2.5|0) |
3 | 0.1111 | 0.15 | -0.22 | 0.35 | |
3.5 | 0.1633 | 0.07 | -0.11 | 0.15 | |
4 | 0.1875 | 0.03 | -0.05 | 0.07 | |
4.5 | 0.1975 | 0.01 | -0.03 | 0.04 | |
5 | 0.2 | 0 | -0.02 | 0.02 | Hochpunkt H(5|0.2) |
5.5 | 0.1983 | -0.01 | -0.01 | 0.01 | |
6 | 0.1944 | -0.01 | 0 | 0.01 | |
6.5 | 0.1893 | -0.01 | 0 | 0 | |
7 | 0.1837 | -0.01 | 0 | 0 | |
7.5 | 0.1778 | -0.01 | 0 | 0 | Wendepunkt W(7.5|0.18) |
8 | 0.1719 | -0.01 | 0 | 0 | |
8.5 | 0.1661 | -0.01 | 0 | 0 | |
9 | 0.1605 | -0.01 | 0 | 0 | |
9.5 | 0.1551 | -0.01 | 0 | 0 | |
10 | 0.15 | -0.01 | 0 | 0 | |
10.5 | 0.1451 | -0.01 | 0 | 0 | |
11 | 0.1405 | -0.01 | 0 | 0 | |
11.5 | 0.1361 | -0.01 | 0 | 0 | |
12 | 0.1319 | -0.01 | 0 | 0 | |
12.5 | 0.128 | -0.01 | 0 | 0 | |
13 | 0.1243 | -0.01 | 0 | 0 | |
13.5 | 0.1207 | -0.01 | 0 | 0 | |
14 | 0.1173 | -0.01 | 0 | 0 | |
14.5 | 0.1141 | -0.01 | 0 | 0 | |
15 | 0.1111 | -0.01 | 0 | 0 | |
15.5 | 0.1082 | -0.01 | 0 | 0 | |
16 | 0.1055 | -0.01 | 0 | 0 | |
16.5 | 0.1028 | -0.01 | 0 | 0 | |
17 | 0.1003 | 0 | 0 | 0 | |
17.5 | 0.098 | 0 | 0 | 0 | |
18 | 0.0957 | 0 | 0 | 0 | |
18.5 | 0.0935 | 0 | 0 | 0 | |
19 | 0.0914 | 0 | 0 | 0 | |
19.5 | 0.0894 | 0 | 0 | 0 | |
20 | 0.0875 | 0 | 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