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Funktion: f(x) = , Df = R\{0}, Wf = (-∞; 0.3704], reelle Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, 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 |
-10 | 0.262 | 0.01 | 0 | 0 | |
-9.5 | 0.2692 | 0.01 | 0 | 0 | |
-9 | 0.2768 | 0.02 | 0 | 0 | |
-8.5 | 0.2849 | 0.02 | 0 | 0 | |
-8 | 0.2933 | 0.02 | 0 | 0 | |
-7.5 | 0.3023 | 0.02 | 0 | 0 | |
-7 | 0.3116 | 0.02 | 0 | 0 | |
-6.5 | 0.3213 | 0.02 | 0 | 0 | |
-6 | 0.3313 | 0.02 | 0 | 0 | |
-5.815 | 0.335 | 0.02 | 0 | 0 | Wendepunkt W(-5.81|0.34) |
-5.5 | 0.3414 | 0.02 | 0 | 0 | |
-5 | 0.3512 | 0.02 | 0 | -0.01 | |
-4.5 | 0.3602 | 0.02 | -0.01 | -0.01 | |
-4 | 0.3672 | 0.01 | -0.01 | -0.02 | |
-3.5 | 0.3704 | 0 | -0.03 | -0.04 | |
-3.485 | 0.3704 | 0 | -0.03 | -0.04 | Hochpunkt H(-3.48|0.37) |
-3 | 0.3662 | -0.02 | -0.05 | -0.07 | |
-2.5 | 0.3479 | -0.06 | -0.1 | -0.14 | |
-2 | 0.3025 | -0.13 | -0.2 | -0.28 | |
-1.5 | 0.2043 | -0.28 | -0.4 | -0.58 | |
-1 | 0 | -0.58 | -0.87 | -1.49 | Nullstelle N(-1|0) |
-0.5 | -0.444 | -1.35 | -2.85 | -10.52 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> -∞ |
0.5 | -0.444 | 1.35 | -2.85 | 10.2 | |
1 | 0 | 0.58 | -0.87 | 1.47 | Nullstelle N(1|0) |
1.5 | 0.2043 | 0.28 | -0.4 | 0.57 | |
2 | 0.3025 | 0.13 | -0.2 | 0.27 | |
2.5 | 0.3479 | 0.06 | -0.1 | 0.14 | |
3 | 0.3662 | 0.02 | -0.05 | 0.07 | |
3.48 | 0.3704 | 0 | -0.03 | 0.04 | Hochpunkt H(3.48|0.37) |
3.5 | 0.3704 | 0 | -0.03 | 0.04 | |
4 | 0.3672 | -0.01 | -0.01 | 0.02 | |
4.5 | 0.3602 | -0.02 | -0.01 | 0.01 | |
5 | 0.3512 | -0.02 | 0 | 0.01 | |
5.5 | 0.3414 | -0.02 | 0 | 0 | |
5.81 | 0.3351 | -0.02 | 0 | 0 | Wendepunkt W(5.81|0.34) |
6 | 0.3313 | -0.02 | 0 | 0 | |
6.5 | 0.3213 | -0.02 | 0 | 0 | |
7 | 0.3116 | -0.02 | 0 | 0 | |
7.5 | 0.3023 | -0.02 | 0 | 0 | |
8 | 0.2933 | -0.02 | 0 | 0 | |
8.5 | 0.2849 | -0.02 | 0 | 0 | |
9 | 0.2768 | -0.02 | 0 | 0 | |
9.5 | 0.2692 | -0.01 | 0 | 0 | |
10 | 0.262 | -0.01 | 0 | 0 | |
Graph: | |||||
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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