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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: | |||||
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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