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Funktion: f(x) = Math.radic;x, Df = [0; +∞), Wf = [0; +∞), Standardquadratwurzelfunktion, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| 0 | 0 | Infinity | Infinity | Infinity | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.5 | 0.7071 | 0.71 | -0.71 | 2.07 | |
| 1 | 1 | 0.5 | -0.25 | 0.37 | |
| 1.5 | 1.2247 | 0.41 | -0.14 | 0.13 | |
| 2 | 1.4142 | 0.35 | -0.09 | 0.07 | |
| 2.5 | 1.5811 | 0.32 | -0.06 | 0.04 | |
| 3 | 1.7321 | 0.29 | -0.05 | 0.02 | |
| 3.5 | 1.8708 | 0.27 | -0.04 | 0.02 | |
| 4 | 2 | 0.25 | -0.03 | 0.01 | |
| 4.5 | 2.1213 | 0.24 | -0.03 | 0.01 | |
| 5 | 2.2361 | 0.22 | -0.02 | 0.01 | |
| 5.5 | 2.3452 | 0.21 | -0.02 | 0.01 | |
| 6 | 2.4495 | 0.2 | -0.02 | 0 | |
| 6.5 | 2.5495 | 0.2 | -0.02 | 0 | |
| 7 | 2.6458 | 0.19 | -0.01 | 0 | |
| 7.5 | 2.7386 | 0.18 | -0.01 | 0 | |
| 8 | 2.8284 | 0.18 | -0.01 | 0 | |
| 8.5 | 2.9155 | 0.17 | -0.01 | 0 | |
| 9 | 3 | 0.17 | -0.01 | 0 | |
| 9.5 | 3.0822 | 0.16 | -0.01 | 0 | |
| 10 | 3.1623 | 0.16 | -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, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann