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Funktion: f(x) = 5√x-4·ln(x), Df = (0; +∞), Wf = [-2.6104; +∞), reelle Funktion, x -> 0: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 |
0.5 | 9.0807 | -12.47 | 28.47 | -113.96 | |
1 | 5 | -5.5 | 6.75 | -13.91 | |
1.5 | 2.88 | -3.29 | 2.88 | -4.02 | |
2 | 1.5259 | -2.23 | 1.56 | -1.66 | |
2.5 | 0.5754 | -1.62 | 0.96 | -0.83 | |
2.89 | 0 | -1.3 | 0.7 | -0.53 | Nullstelle N(2.89|0) |
3 | -0.1286 | -1.22 | 0.65 | -0.47 | |
3.5 | -0.668 | -0.95 | 0.46 | -0.29 | |
4 | -1.0904 | -0.75 | 0.34 | -0.19 | |
4.5 | -1.426 | -0.6 | 0.26 | -0.13 | |
5 | -1.6952 | -0.48 | 0.21 | -0.09 | |
5.5 | -1.9119 | -0.39 | 0.17 | -0.07 | |
6 | -2.0866 | -0.31 | 0.14 | -0.05 | |
6.5 | -2.2269 | -0.25 | 0.11 | -0.04 | |
7 | -2.3385 | -0.2 | 0.1 | -0.03 | |
7.5 | -2.4262 | -0.15 | 0.08 | -0.03 | |
8 | -2.4934 | -0.12 | 0.07 | -0.02 | |
8.5 | -2.5431 | -0.08 | 0.06 | -0.02 | |
9 | -2.5778 | -0.06 | 0.05 | -0.01 | |
9.5 | -2.5993 | -0.03 | 0.05 | -0.01 | |
10 | -2.6093 | -0.01 | 0.04 | -0.01 | |
10.24 | -2.6104 | 0 | 0.04 | -0.01 | Tiefpunkt T(10.24|-2.61) |
10.5 | -2.6092 | 0.01 | 0.04 | -0.01 | |
11 | -2.6 | 0.03 | 0.03 | -0.01 | |
11.5 | -2.583 | 0.04 | 0.03 | -0.01 | |
12 | -2.5587 | 0.06 | 0.03 | -0.01 | |
12.5 | -2.5282 | 0.07 | 0.02 | 0 | |
13 | -2.4918 | 0.08 | 0.02 | 0 | |
13.5 | -2.4503 | 0.09 | 0.02 | 0 | |
14 | -2.4042 | 0.1 | 0.02 | 0 | |
14.5 | -2.3538 | 0.1 | 0.02 | 0 | |
15 | -2.2995 | 0.11 | 0.01 | 0 | |
15.5 | -2.2417 | 0.12 | 0.01 | 0 | |
16 | -2.1807 | 0.12 | 0.01 | 0 | |
16.5 | -2.1168 | 0.13 | 0.01 | 0 | |
17 | -2.0502 | 0.14 | 0.01 | 0 | |
17.5 | -1.9811 | 0.14 | 0.01 | 0 | |
18 | -1.9098 | 0.14 | 0.01 | 0 | |
18.5 | -1.8364 | 0.15 | 0.01 | 0 | |
19 | -1.761 | 0.15 | 0.01 | 0 | |
19.5 | -1.6839 | 0.16 | 0.01 | 0 | |
20 | -1.6052 | 0.16 | 0.01 | 0 | |
20.5 | -1.5249 | 0.16 | 0.01 | 0 | |
21 | -1.4433 | 0.16 | 0.01 | 0 | |
21.5 | -1.3604 | 0.17 | 0 | 0 | |
22 | -1.2763 | 0.17 | 0 | 0 | |
22.5 | -1.191 | 0.17 | 0 | 0 | |
23 | -1.1048 | 0.17 | 0 | 0 | |
23.5 | -1.0176 | 0.18 | 0 | 0 | |
24 | -0.9295 | 0.18 | 0 | 0 | |
24.5 | -0.8406 | 0.18 | 0 | 0 | |
25 | -0.751 | 0.18 | 0 | 0 | |
25.5 | -0.6607 | 0.18 | 0 | 0 | |
26 | -0.5697 | 0.18 | 0 | 0 | |
26.5 | -0.4781 | 0.18 | 0 | 0 | |
27 | -0.3859 | 0.18 | 0 | 0 | |
27.5 | -0.2933 | 0.19 | 0 | 0 | |
28 | -0.2001 | 0.19 | 0 | 0 | |
28.5 | -0.1065 | 0.19 | 0 | 0 | |
29 | -0.0125 | 0.19 | 0 | 0 | |
29.06 | 0 | 0.19 | 0 | 0 | Nullstelle N(29.06|0) |
29.5 | 0.0818 | 0.19 | 0 | 0 | |
30 | 0.1765 | 0.19 | 0 | 0 | |
30.5 | 0.2716 | 0.19 | 0 | 0 | |
31 | 0.3669 | 0.19 | 0 | 0 | |
31.5 | 0.4625 | 0.19 | 0 | 0 | |
32 | 0.5584 | 0.19 | 0 | 0 | |
32.5 | 0.6545 | 0.19 | 0 | 0 | |
33 | 0.7508 | 0.19 | 0 | 0 | |
33.5 | 0.8472 | 0.19 | 0 | 0 | |
34 | 0.9439 | 0.19 | 0 | 0 | |
34.5 | 1.0407 | 0.19 | 0 | 0 | |
35 | 1.1376 | 0.19 | 0 | 0 | |
35.5 | 1.2347 | 0.19 | 0 | 0 | |
36 | 1.3318 | 0.19 | 0 | 0 | |
36.5 | 1.4291 | 0.19 | 0 | 0 | |
37 | 1.5265 | 0.19 | 0 | 0 | |
37.5 | 1.6239 | 0.19 | 0 | 0 | |
38 | 1.7214 | 0.2 | 0 | 0 | |
38.5 | 1.8189 | 0.2 | 0 | 0 | |
39 | 1.9165 | 0.2 | 0 | 0 | |
39.5 | 2.0141 | 0.2 | 0 | 0 | |
40 | 2.1117 | 0.2 | 0 | 0 | |
Graph: | |||||
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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