= arcosh(x), Df = [1; +∞), Wf = [0; +∞), reelle Funktion, x -> +∞: f(x) -> +∞ ->www.michael-buhlmann.de
Funktion: f(x) = = arcosh(x), Df = [1; +∞), Wf = [0; +∞), reelle Funktion, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| 1 | 0 | - | - | - | Nullstelle N(1|0) |
| 1.5 | 0.9624 | 0.89 | -1.07 | 3.11 | |
| 2 | 1.317 | 0.58 | -0.38 | 0.57 | |
| 2.5 | 1.5668 | 0.44 | -0.21 | 0.21 | |
| 3 | 1.7627 | 0.35 | -0.13 | 0.1 | |
| 3.5 | 1.9248 | 0.3 | -0.09 | 0.06 | |
| 4 | 2.0634 | 0.26 | -0.07 | 0.04 | |
| 4.5 | 2.1846 | 0.23 | -0.05 | 0.03 | |
| 5 | 2.2924 | 0.2 | -0.04 | 0.02 | |
| 5.5 | 2.3895 | 0.18 | -0.03 | 0.01 | |
| 6 | 2.4779 | 0.17 | -0.03 | 0.01 | |
| 6.5 | 2.559 | 0.16 | -0.02 | 0.01 | |
| 7 | 2.6339 | 0.14 | -0.02 | 0.01 | |
| 7.5 | 2.7036 | 0.13 | -0.02 | 0 | |
| 8 | 2.7687 | 0.13 | -0.02 | 0 | |
| 8.5 | 2.8297 | 0.12 | -0.01 | 0 | |
| 9 | 2.8873 | 0.11 | -0.01 | 0 | |
| 9.5 | 2.9417 | 0.11 | -0.01 | 0 | |
| 10 | 2.9932 | 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