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Funktionenbibliothek

Funktion: f(x) = , D_f = R, W_f = [4; +∞), Wurzelfunktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->

Wertetabelle:
x	f(x)	f'(x)	f''(x)	f'''(x)	Besondere Kurvenpunkte
-20	14.8337	-0.48	-0.01	0
-19.5	14.5904	-0.49	-0.01	0
-19	14.3452	-0.49	-0.01	0
-18.5	14.098	-0.5	-0.01	0
-18	13.8487	-0.5	-0.01	0
-17.5	13.5974	-0.5	-0.01	0
-17	13.3439	-0.51	-0.01	0
-16.5	13.0882	-0.51	-0.01	0
-16	12.8301	-0.52	-0.01	0
-15.5	12.5697	-0.52	-0.01	0
-15	12.3069	-0.53	-0.01	0
-14.5	12.0415	-0.53	-0.01	0
-14	11.7735	-0.54	-0.01	0
-13.5	11.5028	-0.54	-0.01	0
-13	11.2293	-0.55	-0.01	0
-12.5	10.953	-0.56	-0.01	0
-12	10.6736	-0.56	-0.01	0
-11.5	10.3912	-0.57	-0.01	0
-11	10.1055	-0.57	-0.01	0
-10.5	9.8167	-0.58	-0.01	0
-10	9.5244	-0.59	-0.01	0
-9.5	9.2287	-0.59	-0.01	0
-9	8.9295	-0.6	-0.01	0
-8.5	8.6267	-0.61	-0.01	0
-8	8.3203	-0.62	-0.01	0
-7.5	8.0104	-0.62	-0.01	0
-7	7.697	-0.63	-0.01	0
-6.5	7.3803	-0.64	-0.01	0
-6	7.0607	-0.64	-0.01	0.01
-5.5	6.7387	-0.65	-0.01	0.01
-5	6.4151	-0.65	0	0.01
-4.9	6.3503	-0.65	0	0.01	Wendepunkt W(-4.9|6.35)
-4.5	6.0912	-0.65	0.01	0.02
-4	5.769	-0.64	0.02	0.03
-3.5	5.4514	-0.63	0.03	0.04
-3	5.1426	-0.61	0.06	0.06
-2.5	4.8488	-0.57	0.09	0.08
-2	4.5789	-0.51	0.14	0.11
-1.5	4.3445	-0.42	0.2	0.13
-1	4.1602	-0.31	0.26	0.12
-0.5	4.0412	-0.16	0.31	0.08
0	4	0	0.33	0	Schnittpunkt Sy(0|4) = Tiefpunkt T(0|4)
0.5	4.0412	0.16	0.31	-0.08
1	4.1602	0.31	0.26	-0.12
1.5	4.3445	0.42	0.2	-0.12
2	4.5789	0.51	0.14	-0.11
2.5	4.8488	0.57	0.09	-0.08
3	5.1426	0.61	0.06	-0.06
3.5	5.4514	0.63	0.03	-0.04
4	5.769	0.64	0.02	-0.03
4.5	6.0912	0.65	0.01	-0.02
4.89	6.3438	0.65	0	-0.01	Wendepunkt W(4.89|6.34)
5	6.4151	0.65	0	-0.01
5.5	6.7387	0.65	-0.01	-0.01
6	7.0607	0.64	-0.01	-0.01
6.5	7.3803	0.64	-0.01	0
7	7.697	0.63	-0.01	0
7.5	8.0104	0.62	-0.01	0
8	8.3203	0.62	-0.01	0
8.5	8.6267	0.61	-0.01	0
9	8.9295	0.6	-0.01	0
9.5	9.2287	0.59	-0.01	0
10	9.5244	0.59	-0.01	0
10.5	9.8167	0.58	-0.01	0
11	10.1055	0.57	-0.01	0
11.5	10.3912	0.57	-0.01	0
12	10.6736	0.56	-0.01	0
12.5	10.953	0.56	-0.01	0
13	11.2293	0.55	-0.01	0
13.5	11.5028	0.54	-0.01	0
14	11.7735	0.54	-0.01	0
14.5	12.0415	0.53	-0.01	0
15	12.3069	0.53	-0.01	0
15.5	12.5697	0.52	-0.01	0
16	12.8301	0.52	-0.01	0
16.5	13.0882	0.51	-0.01	0
17	13.3439	0.51	-0.01	0
17.5	13.5974	0.5	-0.01	0
18	13.8487	0.5	-0.01	0
18.5	14.098	0.5	-0.01	0
19	14.3452	0.49	-0.01	0
19.5	14.5904	0.49	-0.01	0
20	14.8337	0.48	-0.01	0
Graph:

Abkürzungen: D_f = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, W_S = Sattelpunkt, W_f = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.

Bearbeiter: Michael Buhlmann

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