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Funktion: f(x) = , Df = R, Wf = [-2.3052; +∞), Wurzelfunktion, Funktion achsensymmetrisch zur Senkrechten x = -2.5, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 3.5303 | -0.4 | -0.04 | -0.02 | |
-9.5 | 3.3247 | -0.42 | -0.05 | -0.02 | |
-9 | 3.1072 | -0.45 | -0.06 | -0.03 | |
-8.5 | 2.8744 | -0.48 | -0.08 | -0.06 | |
-8 | 2.6207 | -0.53 | -0.12 | -0.1 | |
-7.5 | 2.3362 | -0.61 | -0.2 | -0.23 | |
-7 | 2 | -0.75 | -0.4 | -0.69 | |
-6.5 | 1.5536 | -1.1 | -1.3 | -4.53 | |
-6 | 0 | Infinity | Infinity | Infinity | Nullstelle N(-6|0) = Wendepunkt W(-6|0) |
-5.5 | -1.4812 | -0.91 | 1.43 | -4.46 | |
-5 | -1.8171 | -0.5 | 0.48 | -0.72 | |
-4.5 | -2.0206 | -0.33 | 0.27 | -0.24 | |
-4 | -2.1544 | -0.22 | 0.19 | -0.11 | |
-3.5 | -2.2407 | -0.13 | 0.15 | -0.05 | |
-3 | -2.2894 | -0.06 | 0.13 | -0.02 | |
-2.5 | -2.3052 | 0 | 0.13 | 0 | Tiefpunkt T(-2.5|-2.31) |
-2 | -2.2894 | 0.06 | 0.13 | 0.02 | |
-1.5 | -2.2407 | 0.13 | 0.15 | 0.05 | |
-1 | -2.1544 | 0.22 | 0.19 | 0.11 | |
-0.5 | -2.0206 | 0.33 | 0.27 | 0.25 | |
0 | -1.8171 | 0.5 | 0.48 | 0.74 | Schnittpunkt Sy(0|-1.82) |
0.5 | -1.4812 | 0.91 | 1.43 | 4.7 | |
1 | 0 | Infinity | Infinity | Infinity | Nullstelle N(1|0) = Wendepunkt W(1|0) |
1.5 | 1.5536 | 1.1 | -1.3 | 4.29 | |
2 | 2 | 0.75 | -0.4 | 0.67 | |
2.5 | 2.3362 | 0.61 | -0.2 | 0.22 | |
3 | 2.6207 | 0.53 | -0.12 | 0.1 | |
3.5 | 2.8744 | 0.48 | -0.08 | 0.06 | |
4 | 3.1072 | 0.45 | -0.06 | 0.03 | |
4.5 | 3.3247 | 0.42 | -0.05 | 0.02 | |
5 | 3.5303 | 0.4 | -0.04 | 0.02 | |
5.5 | 3.7265 | 0.38 | -0.03 | 0.01 | |
6 | 3.9149 | 0.37 | -0.03 | 0.01 | |
6.5 | 4.0966 | 0.36 | -0.02 | 0.01 | |
7 | 4.2727 | 0.35 | -0.02 | 0.01 | |
7.5 | 4.4437 | 0.34 | -0.02 | 0 | |
8 | 4.6104 | 0.33 | -0.02 | 0 | |
8.5 | 4.7732 | 0.32 | -0.01 | 0 | |
9 | 4.9324 | 0.32 | -0.01 | 0 | |
9.5 | 5.0884 | 0.31 | -0.01 | 0 | |
10 | 5.2415 | 0.3 | -0.01 | 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