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Funktion: f(x) = , Df = R\(3; 6), Wf = [0; +∞), Wurzelfunktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 144.2221 | -24.48 | 2 | 0 | |
-9.5 | 132.2344 | -23.47 | 2 | 0 | |
-9 | 120.7477 | -22.47 | 2 | 0 | |
-8.5 | 109.762 | -21.47 | 2 | 0 | |
-8 | 99.2774 | -20.47 | 2.01 | 0 | |
-7.5 | 89.2941 | -19.47 | 2.01 | 0 | |
-7 | 79.8123 | -18.46 | 2.01 | 0 | |
-6.5 | 70.8321 | -17.46 | 2.01 | 0 | |
-6 | 62.3538 | -16.45 | 2.01 | 0 | |
-5.5 | 54.3777 | -15.45 | 2.01 | 0 | |
-5 | 46.9042 | -14.44 | 2.01 | 0 | |
-4.5 | 39.9335 | -13.44 | 2.01 | 0 | |
-4 | 33.4664 | -12.43 | 2.02 | 0.01 | |
-3.5 | 27.5034 | -11.42 | 2.02 | 0.01 | |
-3 | 22.0454 | -10.41 | 2.02 | 0.01 | |
-2.5 | 17.0935 | -9.4 | 2.03 | 0.01 | |
-2 | 12.6491 | -8.38 | 2.04 | 0.02 | |
-1.5 | 8.7142 | -7.36 | 2.05 | 0.03 | |
-1 | 5.2915 | -6.33 | 2.06 | 0.04 | |
-0.5 | 2.3848 | -5.29 | 2.09 | 0.06 | |
0 | 0 | - | Infinity | Infinity | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
0.5 | 1.854 | 3.17 | -2.18 | -0.15 | |
1 | 3.1623 | 2.06 | -2.28 | -0.29 | |
1.5 | 3.8971 | 0.87 | -2.5 | -0.65 | |
1.82 | 4.042 | 0 | -2.79 | -1.24 | Hochpunkt H(1.82|4.04) |
2 | 4 | -0.5 | -3.06 | -1.92 | |
2.5 | 3.3072 | -2.46 | -5.45 | -11.54 | |
3 | 0 | Infinity | Infinity | Infinity | Nullstelle N(3|0) |
6 | 0 | Infinity | Infinity | Infinity | Nullstelle N(6|0) |
6.5 | 8.5987 | 11.15 | -3.29 | 18.26 | |
6.85 | 12.3917 | 10.71 | -0.01 | 4.4 | Wendepunkt W(6.85|12.39) |
7 | 14 | 10.75 | 0.53 | 2.81 | |
7.5 | 19.4856 | 11.26 | 1.35 | 0.89 | |
8 | 25.2982 | 12.02 | 1.64 | 0.38 | |
8.5 | 31.5188 | 12.88 | 1.78 | 0.19 | |
9 | 38.1838 | 13.79 | 1.86 | 0.11 | |
9.5 | 45.3121 | 14.73 | 1.9 | 0.07 | |
10 | 52.915 | 15.69 | 1.93 | 0.04 | |
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