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Funktion: f(x) = , Df = R, Wf = [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: Df = (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, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann