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Funktion: f(x) = x2·ln(x+5)-x3·ln(x+2), Df = (-2; +∞), Wf = (-∞ 1.5401], reelle Funktion, x -> -2: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-2 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -2 |
-1.555 | -0.0535 | 11.18 | -58.68 | 261.79 | Nullstelle N(-1.55|-0.05) |
-1.5 | 0.4793 | 8.31 | -46.13 | 193.2 | |
-1.18 | 1.5401 | 0.03 | -12.69 | 53.36 | Hochpunkt H(-1.18|1.54) |
-1 | 1.3863 | -1.52 | -5.29 | 30.68 | |
-0.765 | 0.9392 | -2.08 | -0.04 | 15.38 | Wendepunkt W(-0.76|0.94) |
-0.5 | 0.4267 | -1.67 | 2.71 | 6.06 | |
0 | 0 | 0 | 3.22 | -2.99 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
0.5 | 0.3117 | 1.01 | 0.44 | -7.78 | |
0.55 | 0.3627 | 1.02 | 0.04 | -8.14 | Wendepunkt W(0.55|0.36) |
1 | 0.6931 | 0.12 | -4.26 | -10.84 | |
1.025 | 0.6948 | 0.01 | -4.53 | -10.96 | Hochpunkt H(1.02|0.69) |
1.495 | 0.0006 | -3.41 | -10.18 | -13 | Nullstelle N(1.5|0) |
1.5 | -0.0165 | -3.46 | -10.24 | -13.02 | |
2 | -3.3067 | -10.28 | -17.18 | -14.69 | |
2.5 | -10.9081 | -20.77 | -24.87 | -16.03 | |
3 | -24.7398 | -35.25 | -33.17 | -17.15 | |
3.5 | -46.8753 | -54.02 | -41.99 | -18.1 | |
4 | -79.517 | -77.32 | -51.25 | -18.93 | |
4.5 | -124.9793 | -105.34 | -60.9 | -19.67 | |
5 | -185.6741 | -138.27 | -70.9 | -20.32 | |
5.5 | -264.1004 | -176.29 | -81.21 | -20.92 | |
6 | -362.8351 | -219.53 | -91.8 | -21.46 | |
6.5 | -484.5265 | -268.14 | -102.66 | -21.96 | |
7 | -631.8876 | -322.23 | -113.75 | -22.42 | |
7.5 | -807.6915 | -381.93 | -125.07 | -22.85 | |
8 | -1014.7668 | -447.33 | -136.59 | -23.25 | |
8.5 | -1255.994 | -518.55 | -148.31 | -23.62 | |
9 | -1534.302 | -595.67 | -160.21 | -23.97 | |
9.5 | -1852.6654 | -678.79 | -172.28 | -24.31 | |
10 | -2214.1016 | -767.98 | -184.51 | -24.63 | |
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