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Funktion: f(x) = , Df = (-5; +∞), Wf = R, Wurzelfunktion, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-5 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -5 mit: x -> -5+: f(x) -> +∞ |
-4.5 | 15.0997 | -17.24 | 50.96 | -246.05 | |
-4 | 10 | -6.25 | 9.03 | -22.13 | |
-3.5 | 7.6766 | -3.5 | 3.29 | -5.39 | |
-3 | 6.2492 | -2.34 | 1.61 | -1.98 | |
-2.5 | 5.2443 | -1.73 | 0.93 | -0.91 | |
-2 | 4.4787 | -1.36 | 0.59 | -0.48 | |
-1.5 | 3.8648 | -1.11 | 0.41 | -0.28 | |
-1 | 3.3542 | -0.94 | 0.29 | -0.18 | |
-0.5 | 2.9182 | -0.81 | 0.22 | -0.12 | |
0 | 2.5381 | -0.71 | 0.17 | -0.08 | Schnittpunkt Sy(0|2.54) |
0.5 | 2.2013 | -0.64 | 0.14 | -0.06 | |
1 | 1.899 | -0.57 | 0.11 | -0.04 | |
1.5 | 1.6246 | -0.52 | 0.09 | -0.03 | |
2 | 1.3733 | -0.48 | 0.08 | -0.03 | |
2.5 | 1.1414 | -0.45 | 0.07 | -0.02 | |
3 | 0.926 | -0.42 | 0.06 | -0.02 | |
3.5 | 0.7248 | -0.39 | 0.05 | -0.01 | |
4 | 0.5359 | -0.37 | 0.04 | -0.01 | |
4.5 | 0.3578 | -0.35 | 0.04 | -0.01 | |
5 | 0.1892 | -0.33 | 0.03 | -0.01 | |
5.5 | 0.029 | -0.31 | 0.03 | -0.01 | |
5.59 | 0 | -0.31 | 0.03 | -0.01 | Nullstelle N(5.59|0) |
6 | -0.1235 | -0.3 | 0.03 | -0.01 | |
6.5 | -0.2693 | -0.29 | 0.02 | 0 | |
7 | -0.4089 | -0.27 | 0.02 | 0 | |
7.5 | -0.5429 | -0.26 | 0.02 | 0 | |
8 | -0.6718 | -0.25 | 0.02 | 0 | |
8.5 | -0.796 | -0.24 | 0.02 | 0 | |
9 | -0.916 | -0.24 | 0.02 | 0 | |
9.5 | -1.0319 | -0.23 | 0.01 | 0 | |
10 | -1.1443 | -0.22 | 0.01 | 0 | |
10.5 | -1.2532 | -0.21 | 0.01 | 0 | |
11 | -1.3589 | -0.21 | 0.01 | 0 | |
11.5 | -1.4617 | -0.2 | 0.01 | 0 | |
12 | -1.5617 | -0.2 | 0.01 | 0 | |
12.5 | -1.6591 | -0.19 | 0.01 | 0 | |
13 | -1.7541 | -0.19 | 0.01 | 0 | |
13.5 | -1.8469 | -0.18 | 0.01 | 0 | |
14 | -1.9374 | -0.18 | 0.01 | 0 | |
14.5 | -2.026 | -0.18 | 0.01 | 0 | |
15 | -2.1125 | -0.17 | 0.01 | 0 | |
15.5 | -2.1973 | -0.17 | 0.01 | 0 | |
16 | -2.2804 | -0.16 | 0.01 | 0 | |
16.5 | -2.3618 | -0.16 | 0.01 | 0 | |
17 | -2.4416 | -0.16 | 0.01 | 0 | |
17.5 | -2.5199 | -0.16 | 0.01 | 0 | |
18 | -2.5968 | -0.15 | 0.01 | 0 | |
18.5 | -2.6724 | -0.15 | 0.01 | 0 | |
19 | -2.7467 | -0.15 | 0 | 0 | |
19.5 | -2.8197 | -0.14 | 0 | 0 | |
20 | -2.8915 | -0.14 | 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