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Funktion: f(x) = , Df = R\{-4}, Wf = (-∞; 1.6875], gebrochen rationale Funktion, x -> -∞: f(x) -> 1.5 = y als Grenzkurve, x -> +∞: f(x) -> 1.5 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | 1.2656 | -0.02 | 0 | 0 | |
-19.5 | 1.2565 | -0.02 | 0 | 0 | |
-19 | 1.2467 | -0.02 | 0 | 0 | |
-18.5 | 1.236 | -0.02 | 0 | 0 | |
-18 | 1.2245 | -0.02 | 0 | 0 | |
-17.5 | 1.2119 | -0.03 | 0 | 0 | |
-17 | 1.1982 | -0.03 | -0.01 | 0 | |
-16.5 | 1.1832 | -0.03 | -0.01 | 0 | |
-16 | 1.1667 | -0.03 | -0.01 | 0 | |
-15.5 | 1.1484 | -0.04 | -0.01 | 0 | |
-15 | 1.1281 | -0.04 | -0.01 | 0 | |
-14.5 | 1.1054 | -0.05 | -0.01 | 0 | |
-14 | 1.08 | -0.05 | -0.01 | 0 | |
-13.5 | 1.0512 | -0.06 | -0.02 | -0.01 | |
-13 | 1.0185 | -0.07 | -0.02 | -0.01 | |
-12.5 | 0.981 | -0.08 | -0.02 | -0.01 | |
-12 | 0.9375 | -0.09 | -0.03 | -0.01 | |
-11.5 | 0.8867 | -0.11 | -0.04 | -0.02 | |
-11 | 0.8265 | -0.13 | -0.05 | -0.02 | |
-10.5 | 0.7544 | -0.16 | -0.06 | -0.03 | |
-10 | 0.6667 | -0.19 | -0.08 | -0.05 | |
-9.5 | 0.5579 | -0.24 | -0.11 | -0.08 | |
-9 | 0.42 | -0.31 | -0.16 | -0.12 | |
-8.5 | 0.2407 | -0.41 | -0.24 | -0.2 | |
-8 | 0 | -0.56 | -0.38 | -0.35 | Nullstelle N(-8|0) |
-7.5 | -0.3367 | -0.8 | -0.62 | -0.67 | |
-7 | -0.8333 | -1.22 | -1.11 | -1.41 | |
-6.5 | -1.62 | -2.02 | -2.23 | -3.43 | |
-6 | -3 | -3.75 | -5.25 | -10.19 | |
-5.5 | -5.8333 | -8.44 | -16 | -41.82 | |
-5 | -13.5 | -27 | -78 | -309.84 | |
-4.5 | -52.5 | -204.04 | -1200.2 | -9747.38 | |
-4 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -4 ohne Vorzeichenwechsel: x -> -4-: f(x) -> -∞, x -> -4+: f(x) -> -∞ |
-3.5 | -40.5 | 180.04 | -1104.19 | 8709.97 | |
-3 | -7.5 | 21 | -66 | 266.63 | |
-2.5 | -1.8333 | 5.78 | -12.44 | 34.08 | |
-2 | 0 | 2.25 | -3.75 | 7.82 | Nullstelle N(-2|0) |
-1.5 | 0.78 | 1.06 | -1.46 | 2.48 | |
-1 | 1.1667 | 0.56 | -0.67 | 0.96 | |
-0.5 | 1.3776 | 0.31 | -0.34 | 0.43 | |
0 | 1.5 | 0.19 | -0.19 | 0.21 | Schnittpunkt Sy(0|1.5) |
0.5 | 1.5741 | 0.12 | -0.11 | 0.11 | |
1 | 1.62 | 0.07 | -0.07 | 0.06 | |
1.5 | 1.6488 | 0.05 | -0.04 | 0.04 | |
2 | 1.6667 | 0.03 | -0.03 | 0.02 | |
2.5 | 1.6775 | 0.02 | -0.02 | 0.01 | |
3 | 1.6837 | 0.01 | -0.01 | 0.01 | |
3.5 | 1.6867 | 0 | -0.01 | 0.01 | |
4 | 1.6875 | 0 | -0.01 | 0 | Hochpunkt H(4|1.69) |
4.5 | 1.6869 | 0 | 0 | 0 | |
5 | 1.6852 | 0 | 0 | 0 | |
5.5 | 1.6828 | -0.01 | 0 | 0 | |
6 | 1.68 | -0.01 | 0 | 0 | |
6.5 | 1.6769 | -0.01 | 0 | 0 | |
7 | 1.6736 | -0.01 | 0 | 0 | |
7.5 | 1.6701 | -0.01 | 0 | 0 | |
8 | 1.6667 | -0.01 | 0 | 0 | Wendepunkt W(8|1.67) |
8.5 | 1.6632 | -0.01 | 0 | 0 | |
9 | 1.6598 | -0.01 | 0 | 0 | |
9.5 | 1.6564 | -0.01 | 0 | 0 | |
10 | 1.6531 | -0.01 | 0 | 0 | |
10.5 | 1.6498 | -0.01 | 0 | 0 | |
11 | 1.6467 | -0.01 | 0 | 0 | |
11.5 | 1.6436 | -0.01 | 0 | 0 | |
12 | 1.6406 | -0.01 | 0 | 0 | |
12.5 | 1.6377 | -0.01 | 0 | 0 | |
13 | 1.6349 | -0.01 | 0 | 0 | |
13.5 | 1.6322 | -0.01 | 0 | 0 | |
14 | 1.6296 | -0.01 | 0 | 0 | |
14.5 | 1.6271 | 0 | 0 | 0 | |
15 | 1.6247 | 0 | 0 | 0 | |
15.5 | 1.6223 | 0 | 0 | 0 | |
16 | 1.62 | 0 | 0 | 0 | |
16.5 | 1.6178 | 0 | 0 | 0 | |
17 | 1.6156 | 0 | 0 | 0 | |
17.5 | 1.6136 | 0 | 0 | 0 | |
18 | 1.6116 | 0 | 0 | 0 | |
18.5 | 1.6096 | 0 | 0 | 0 | |
19 | 1.6078 | 0 | 0 | 0 | |
19.5 | 1.6059 | 0 | 0 | 0 | |
20 | 1.6042 | 0 | 0 | 0 | |
Graph: | |||||
Graph(en) der Asymptote(n), Grenzkurve(n).
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