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Funktion: f(x) = ln4(x2), Df = R\{0}, Wf = R, reelle Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 449.762 | -78.13 | 2.37 | 0.61 | |
-9.5 | 411.005 | -76.87 | 2.69 | 0.7 | |
-9 | 372.9218 | -75.43 | 3.06 | 0.8 | |
-8.5 | 335.6053 | -73.8 | 3.49 | 0.92 | |
-8 | 299.1623 | -71.93 | 3.98 | 1.05 | |
-7.5 | 263.7161 | -69.8 | 4.55 | 1.23 | |
-7 | 229.4094 | -67.37 | 5.21 | 1.43 | |
-6.5 | 196.4083 | -64.57 | 5.99 | 1.67 | |
-6 | 164.9069 | -61.36 | 6.9 | 1.96 | |
-5.5 | 135.1328 | -57.65 | 7.96 | 2.32 | |
-5 | 107.3537 | -53.36 | 9.22 | 2.72 | |
-4.5 | 81.8843 | -48.39 | 10.7 | 3.18 | |
-4 | 59.0938 | -42.63 | 12.4 | 3.65 | |
-3.5 | 39.409 | -35.95 | 14.33 | 3.99 | |
-3 | 23.3076 | -28.29 | 16.32 | 3.84 | |
-2.5 | 11.2785 | -19.69 | 17.91 | 2.13 | |
-2 | 3.6934 | -10.66 | 17.73 | -4.01 | |
-1.5 | 0.4324 | -2.84 | 12.13 | -20.61 | |
-1 | 0 | 0 | 0 | 0.1 | Nullstelle N(-1|0) = Tiefpunkt T(-1|0) |
-0.5 | 3.6934 | 42.63 | 454.24 | 4696.82 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> +∞, x -> 0+: f(x) -> +∞ |
0.5 | 3.6934 | -42.63 | 454.24 | -4671.83 | |
1 | 0 | 0 | 0 | 0.1 | Nullstelle N(1|0) = Tiefpunkt T(1|0) |
1.5 | 0.4324 | 2.84 | 12.13 | 20.59 | |
2 | 3.6934 | 10.66 | 17.73 | 4 | |
2.5 | 11.2785 | 19.69 | 17.91 | -2.13 | |
3 | 23.3076 | 28.29 | 16.32 | -3.84 | |
3.5 | 39.409 | 35.95 | 14.33 | -3.99 | |
4 | 59.0938 | 42.63 | 12.4 | -3.65 | |
4.5 | 81.8843 | 48.39 | 10.7 | -3.18 | |
5 | 107.3537 | 53.36 | 9.22 | -2.72 | |
5.5 | 135.1328 | 57.65 | 7.96 | -2.31 | |
6 | 164.9069 | 61.36 | 6.9 | -1.97 | |
6.5 | 196.4083 | 64.57 | 5.99 | -1.67 | |
7 | 229.4094 | 67.37 | 5.21 | -1.43 | |
7.5 | 263.7161 | 69.8 | 4.55 | -1.23 | |
8 | 299.1623 | 71.93 | 3.98 | -1.06 | |
8.5 | 335.6053 | 73.8 | 3.49 | -0.91 | |
9 | 372.9218 | 75.43 | 3.06 | -0.79 | |
9.5 | 411.005 | 76.87 | 2.69 | -0.69 | |
10 | 449.762 | 78.13 | 2.37 | -0.61 | |
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