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Funktion: f(x) = , Df = [-5; +∞), Wf = [-3.3559; +∞), Wurzelfunktion, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-5 | 43.3013 | Infinity | Infinity | Infinity | |
-4.5 | 28.3383 | -18.85 | 11.95 | -31.23 | |
-4 | 20 | -15 | 5.5 | -4.24 | |
-3.5 | 13.1264 | -12.57 | 4.5 | -0.57 | |
-3 | 7.3967 | -10.34 | 4.5 | 0.42 | |
-2.5 | 2.799 | -8.02 | 4.81 | 0.75 | |
-2.11 | 0.0439 | -6.09 | 5.12 | 0.85 | Nullstelle N(-2.11|0.04) |
-2 | -0.5943 | -5.52 | 5.22 | 0.87 | |
-1.5 | -2.6823 | -2.8 | 5.66 | 0.9 | |
-1.03 | -3.3559 | -0.04 | 6.09 | 0.9 | Tiefpunkt T(-1.03|-3.36) |
-1 | -3.3542 | 0.15 | 6.12 | 0.9 | |
-0.5 | -2.4973 | 3.32 | 6.56 | 0.88 | |
0 | 0 | 6.71 | 7 | 0.86 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
0.5 | 4.2467 | 10.31 | 7.42 | 0.83 | |
1 | 10.3485 | 14.13 | 7.83 | 0.81 | |
1.5 | 18.4078 | 18.14 | 8.23 | 0.78 | |
2 | 28.5236 | 22.35 | 8.61 | 0.75 | |
2.5 | 40.7919 | 26.75 | 8.98 | 0.73 | |
3 | 55.3055 | 31.33 | 9.34 | 0.71 | |
3.5 | 72.1543 | 36.09 | 9.69 | 0.69 | |
4 | 91.4256 | 41.02 | 10.03 | 0.67 | |
4.5 | 113.2044 | 46.12 | 10.36 | 0.65 | |
5 | 137.5729 | 51.38 | 10.68 | 0.63 | |
5.5 | 164.6117 | 56.8 | 10.99 | 0.62 | |
6 | 194.3989 | 62.37 | 11.3 | 0.6 | |
6.5 | 227.0109 | 68.1 | 11.6 | 0.59 | |
7 | 262.5223 | 73.97 | 11.89 | 0.58 | |
7.5 | 301.006 | 79.99 | 12.17 | 0.56 | |
8 | 342.5332 | 86.14 | 12.45 | 0.55 | |
8.5 | 387.1739 | 92.44 | 12.73 | 0.54 | |
9 | 434.9963 | 98.87 | 13 | 0.53 | |
9.5 | 486.0676 | 105.44 | 13.26 | 0.52 | |
10 | 540.4536 | 112.13 | 13.52 | 0.51 | |
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