www.michael-buhlmann.de
Funktion: f(x) = ln(x2+4)/2, Df = R, Wf = [ln(2); +∞), 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 | 2.3222 | -0.1 | -0.01 | 0 | |
-9.5 | 2.273 | -0.1 | -0.01 | 0 | |
-9 | 2.2213 | -0.11 | -0.01 | 0 | |
-8.5 | 2.167 | -0.11 | -0.01 | 0 | |
-8 | 2.1098 | -0.12 | -0.01 | 0 | |
-7.5 | 2.0493 | -0.12 | -0.01 | 0 | |
-7 | 1.9851 | -0.13 | -0.02 | 0 | |
-6.5 | 1.917 | -0.14 | -0.02 | 0 | |
-6 | 1.8444 | -0.15 | -0.02 | 0 | |
-5.5 | 1.7668 | -0.16 | -0.02 | -0.01 | |
-5 | 1.6836 | -0.17 | -0.02 | -0.01 | |
-4.5 | 1.5942 | -0.19 | -0.03 | -0.01 | |
-4 | 1.4979 | -0.2 | -0.03 | 0 | |
-3.5 | 1.394 | -0.22 | -0.03 | 0 | |
-3 | 1.2825 | -0.23 | -0.03 | 0.01 | |
-2.5 | 1.1636 | -0.24 | -0.02 | 0.03 | |
-2 | 1.0397 | -0.25 | 0 | 0.06 | Wendepunkt W(-2|1.04) |
-1.5 | 0.9163 | -0.24 | 0.04 | 0.12 | |
-1 | 0.8047 | -0.2 | 0.12 | 0.18 | |
-0.5 | 0.7235 | -0.12 | 0.21 | 0.15 | |
0 | 0.6931 | 0 | 0.25 | 0 | Schnittpunkt Sy(0|0.69) = Tiefpunkt T(0|0.69) |
0.5 | 0.7235 | 0.12 | 0.21 | -0.15 | |
1 | 0.8047 | 0.2 | 0.12 | -0.18 | |
1.5 | 0.9163 | 0.24 | 0.04 | -0.12 | |
2 | 1.0397 | 0.25 | 0 | -0.06 | Wendepunkt W(2|1.04) |
2.5 | 1.1636 | 0.24 | -0.02 | -0.03 | |
3 | 1.2825 | 0.23 | -0.03 | -0.01 | |
3.5 | 1.394 | 0.22 | -0.03 | 0 | |
4 | 1.4979 | 0.2 | -0.03 | 0 | |
4.5 | 1.5942 | 0.19 | -0.03 | 0.01 | |
5 | 1.6836 | 0.17 | -0.02 | 0.01 | |
5.5 | 1.7668 | 0.16 | -0.02 | 0 | |
6 | 1.8444 | 0.15 | -0.02 | 0 | |
6.5 | 1.917 | 0.14 | -0.02 | 0 | |
7 | 1.9851 | 0.13 | -0.02 | 0 | |
7.5 | 2.0493 | 0.12 | -0.01 | 0 | |
8 | 2.1098 | 0.12 | -0.01 | 0 | |
8.5 | 2.167 | 0.11 | -0.01 | 0 | |
9 | 2.2213 | 0.11 | -0.01 | 0 | |
9.5 | 2.273 | 0.1 | -0.01 | 0 | |
10 | 2.3222 | 0.1 | -0.01 | 0 | |
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