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Funktion: f(x) = , Df = R\{0}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> 0 = y als Grenzkurve, x -> +∞: f(x) -> 0 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | 0.0064 | 0 | 0 | 0 | |
-19.5 | 0.0067 | 0 | 0 | 0 | |
-19 | 0.007 | 0 | 0 | 0 | |
-18.5 | 0.0073 | 0 | 0 | 0 | |
-18 | 0.0077 | 0 | 0 | 0 | |
-17.5 | 0.0081 | 0 | 0 | 0 | |
-17 | 0.0085 | 0 | 0 | 0 | |
-16.5 | 0.009 | 0 | 0 | 0 | |
-16 | 0.0095 | 0 | 0 | 0 | |
-15.5 | 0.0101 | 0 | 0 | 0 | |
-15 | 0.0107 | 0 | 0 | 0 | |
-14.5 | 0.0113 | 0 | 0 | 0 | |
-14 | 0.012 | 0 | 0 | 0 | |
-13.5 | 0.0128 | 0 | 0 | 0 | |
-13 | 0.0137 | 0 | 0 | 0 | |
-12.5 | 0.0146 | 0 | 0 | 0 | |
-12 | 0.0156 | 0 | 0 | 0 | |
-11.5 | 0.0168 | 0 | 0 | 0 | |
-11 | 0.018 | 0 | 0 | 0 | |
-10.5 | 0.0194 | 0 | 0 | 0 | |
-10 | 0.021 | 0 | 0 | 0 | |
-9.5 | 0.0227 | 0 | 0 | 0 | |
-9 | 0.0247 | 0 | 0 | 0 | |
-8.5 | 0.0269 | 0 | 0 | 0 | |
-8 | 0.0293 | 0.01 | 0 | 0 | |
-7.5 | 0.032 | 0.01 | 0 | 0 | |
-7 | 0.035 | 0.01 | 0 | 0 | |
-6.5 | 0.0382 | 0.01 | 0 | 0 | |
-6 | 0.0417 | 0.01 | 0 | 0 | Wendepunkt W(-6|0.04) |
-5.5 | 0.0451 | 0.01 | 0 | -0.01 | |
-5 | 0.048 | 0 | -0.01 | -0.01 | |
-4.502 | 0.0494 | 0 | -0.01 | -0.03 | Hochpunkt H(-4.5|0.05) |
-4.5 | 0.0494 | 0 | -0.01 | -0.03 | |
-4 | 0.0469 | -0.01 | -0.04 | -0.06 | |
-3.5 | 0.035 | -0.04 | -0.09 | -0.16 | |
-3 | 0 | -0.11 | -0.22 | -0.45 | Nullstelle N(-3|0) |
-2.5 | -0.096 | -0.31 | -0.65 | -1.48 | |
-2 | -0.375 | -0.94 | -2.25 | -6.21 | |
-1.5 | -1.3333 | -3.56 | -10.67 | -38.08 | |
-1 | -6 | -21 | -90 | -470.9 | |
-0.5 | -60 | -384.02 | -3168.13 | -32653.27 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 mit Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> +∞ |
0.5 | 84 | -480.02 | 3744.15 | -36432.26 | |
1 | 12 | -33 | 126 | -608.42 | |
1.5 | 4 | -7.11 | 17.78 | -56.67 | |
2 | 1.875 | -2.44 | 4.5 | -10.66 | |
2.5 | 1.056 | -1.08 | 1.57 | -2.94 | |
3 | 0.6667 | -0.56 | 0.67 | -1.04 | |
3.5 | 0.4548 | -0.32 | 0.33 | -0.43 | |
4 | 0.3281 | -0.2 | 0.18 | -0.2 | |
4.5 | 0.2469 | -0.13 | 0.1 | -0.1 | |
5 | 0.192 | -0.09 | 0.06 | -0.06 | |
5.5 | 0.1533 | -0.07 | 0.04 | -0.03 | |
6 | 0.125 | -0.05 | 0.03 | -0.02 | |
6.5 | 0.1038 | -0.04 | 0.02 | -0.01 | |
7 | 0.0875 | -0.03 | 0.01 | -0.01 | |
7.5 | 0.0747 | -0.02 | 0.01 | -0.01 | |
8 | 0.0645 | -0.02 | 0.01 | 0 | |
8.5 | 0.0562 | -0.01 | 0.01 | 0 | |
9 | 0.0494 | -0.01 | 0 | 0 | |
9.5 | 0.0437 | -0.01 | 0 | 0 | |
10 | 0.039 | -0.01 | 0 | 0 | |
10.5 | 0.035 | -0.01 | 0 | 0 | |
11 | 0.0316 | -0.01 | 0 | 0 | |
11.5 | 0.0286 | -0.01 | 0 | 0 | |
12 | 0.026 | 0 | 0 | 0 | |
12.5 | 0.0238 | 0 | 0 | 0 | |
13 | 0.0218 | 0 | 0 | 0 | |
13.5 | 0.0201 | 0 | 0 | 0 | |
14 | 0.0186 | 0 | 0 | 0 | |
14.5 | 0.0172 | 0 | 0 | 0 | |
15 | 0.016 | 0 | 0 | 0 | |
15.5 | 0.0149 | 0 | 0 | 0 | |
16 | 0.0139 | 0 | 0 | 0 | |
16.5 | 0.013 | 0 | 0 | 0 | |
17 | 0.0122 | 0 | 0 | 0 | |
17.5 | 0.0115 | 0 | 0 | 0 | |
18 | 0.0108 | 0 | 0 | 0 | |
18.5 | 0.0102 | 0 | 0 | 0 | |
19 | 0.0096 | 0 | 0 | 0 | |
19.5 | 0.0091 | 0 | 0 | 0 | |
20 | 0.0086 | 0 | 0 | 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