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Funktion: f(x) = , Df = R, Wf = [0.9634; +∞), reelle Funktion, x -> -∞: f(x) -> -x√3 = y als Grenzkurve, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 17.3205 | -1.73 | 0 | 0 | |
-9.5 | 16.4545 | -1.73 | 0 | 0 | |
-9 | 15.5885 | -1.73 | 0 | 0 | |
-8.5 | 14.7224 | -1.73 | 0 | 0 | |
-8 | 13.8564 | -1.73 | 0 | 0 | |
-7.5 | 12.9904 | -1.73 | 0 | 0 | |
-7 | 12.1244 | -1.73 | 0 | 0 | |
-6.5 | 11.2584 | -1.73 | 0 | 0 | |
-6 | 10.3924 | -1.73 | 0 | 0 | |
-5.5 | 9.5265 | -1.73 | 0 | 0 | |
-5 | 8.6606 | -1.73 | 0 | 0 | |
-4.5 | 7.7949 | -1.73 | 0 | 0 | |
-4 | 6.9295 | -1.73 | 0 | 0 | |
-3.5 | 6.0647 | -1.73 | 0 | 0.01 | |
-3 | 5.2009 | -1.73 | 0.01 | 0.01 | |
-2.5 | 4.3396 | -1.72 | 0.02 | 0.03 | |
-2 | 3.4836 | -1.7 | 0.05 | 0.09 | |
-1.5 | 2.6407 | -1.66 | 0.13 | 0.3 | |
-1 | 1.8352 | -1.53 | 0.45 | 1.25 | |
-0.5 | 1.1647 | -1.03 | 1.93 | 5.41 | |
-0.15 | 0.9634 | 0 | 3.56 | 0.48 | Tiefpunkt T(-0.15|0.96) |
0 | 1 | 0.5 | 3.25 | -4.48 | Schnittpunkt Sy(0|1) |
0.5 | 1.5488 | 1.5 | 1.02 | -2.38 | |
1 | 2.3913 | 1.82 | 0.43 | -0.41 | |
1.5 | 3.3514 | 2.01 | 0.36 | 0.03 | |
2 | 4.4033 | 2.2 | 0.42 | 0.21 | |
2.5 | 5.5617 | 2.44 | 0.56 | 0.36 | |
3 | 6.8619 | 2.78 | 0.78 | 0.52 | |
3.5 | 8.3586 | 3.24 | 1.09 | 0.72 | |
4 | 10.1291 | 3.88 | 1.51 | 0.97 | |
4.5 | 12.2787 | 4.77 | 2.06 | 1.27 | |
5 | 14.947 | 5.97 | 2.78 | 1.64 | |
5.5 | 18.3151 | 7.58 | 3.71 | 2.08 | |
6 | 22.6148 | 9.72 | 4.88 | 2.64 | |
6.5 | 28.1406 | 12.51 | 6.36 | 3.34 | |
7 | 35.2652 | 16.14 | 8.24 | 4.24 | |
7.5 | 44.4611 | 20.84 | 10.63 | 5.39 | |
8 | 56.329 | 26.89 | 13.68 | 6.89 | |
8.5 | 71.6346 | 34.66 | 17.58 | 8.81 | |
9 | 91.3569 | 44.64 | 22.56 | 11.3 | |
9.5 | 116.7496 | 57.46 | 28.96 | 14.49 | |
10 | 149.4204 | 73.91 | 37.17 | 18.6 | |
Graph: | |||||
Graph(en) der Asymptote(n), Grenzkurve(n).
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