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Funktion: f(x) = 7·ln(3x)-3x, Df = (0; +∞), Wf = (-∞; 6.6214], reelle Funktion, x -> 0: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 |
0.394 | 0 | 14.77 | -45.09 | 227.17 | Nullstelle N(0.39|0) |
0.5 | 1.3383 | 11 | -28 | 111.33 | |
1 | 4.6903 | 4 | -7 | 13.96 | |
1.5 | 6.0285 | 1.67 | -3.11 | 4.14 | |
2 | 6.5423 | 0.5 | -1.75 | 1.75 | |
2.332 | 6.6214 | 0 | -1.29 | 1.1 | Hochpunkt H(2.33|6.62) |
2.5 | 6.6043 | -0.2 | -1.12 | 0.89 | |
3 | 6.3806 | -0.67 | -0.78 | 0.52 | |
3.5 | 5.9596 | -1 | -0.57 | 0.33 | |
4 | 5.3943 | -1.25 | -0.44 | 0.22 | |
4.5 | 4.7188 | -1.44 | -0.35 | 0.15 | |
5 | 3.9564 | -1.6 | -0.28 | 0.11 | |
5.5 | 3.1235 | -1.73 | -0.23 | 0.08 | |
6 | 2.2326 | -1.83 | -0.19 | 0.06 | |
6.5 | 1.2929 | -1.92 | -0.17 | 0.05 | |
7 | 0.3117 | -2 | -0.14 | 0.04 | |
7.154 | 0 | -2.02 | -0.14 | 0.04 | Nullstelle N(7.15|0) |
7.5 | -0.7054 | -2.07 | -0.12 | 0.03 | |
8 | -1.7536 | -2.12 | -0.11 | 0.03 | |
8.5 | -2.8293 | -2.18 | -0.1 | 0.02 | |
9 | -3.9291 | -2.22 | -0.09 | 0.02 | |
9.5 | -5.0507 | -2.26 | -0.08 | 0.02 | |
10 | -6.1916 | -2.3 | -0.07 | 0.01 | |
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