www.michael-buhlmann.de
Funktion: f(x) = sin(1/x), Df = R\{0}, Wf = [-1; 1], reelle Funktion, Funktion punktsymmetrisch zu O(0|0), x -> 0: f(x) -> -1, ... 1 ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -2 | -0.4794 | -0.22 | -0.19 | -0.23 | |
| -1.5 | -0.6184 | -0.35 | -0.34 | -0.37 | |
| -1 | -0.8415 | -0.54 | -0.24 | 2.36 | |
| -0.929 | -0.8803 | -0.55 | 0 | 4.57 | Wendepunkt W(-0.93|-0.88) |
| -0.637 | -1 | 0 | 6.07 | 57.44 | Tiefpunkt T(-0.64|-1) |
| -0.5 | -0.9093 | 1.66 | 21.21 | 188.68 | |
| -0.319 | -0.0068 | 9.83 | 62.26 | -371.57 | Nullstelle N(-0.32|-0.01) |
| -0.275 | 0.4748 | 11.64 | 1.6 | -2973.79 | Wendepunkt W(-0.28|0.47) |
| -0.213 | 0.9998 | 0.38 | -482.13 | -13896.98 | Hochpunkt H(-0.21|1) |
| -0.16 | 0.0332 | -39.03 | -538.29 | 50692.67 | Nullstelle N(-0.16|0.03) |
| -0.153 | -0.2501 | -41.35 | -83.85 | 85570.09 | Wendepunkt W(-0.15|-0.25) |
| -0.128 | -0.9991 | -2.5 | 3682.13 | 180116.56 | Tiefpunkt T(-0.13|-1) |
| -0.107 | -0.0789 | 86.97 | 2223.15 | -623201.92 | Nullstelle N(-0.11|-0.08) |
| -0.104 | 0.1895 | 90.64 | 119.73 | -858421.47 | Wendepunkt W(-0.1|0.19) |
| [...] | |||||
| 0.103 | -0.2802 | 90.34 | 738.69 | -858421.47 | Wendepunkt W(0.1|-0.28) |
| 0.106 | -0.0092 | 88.89 | -1599.95 | -623201.92 | Nullstelle N(0.11|-0.01) |
| 0.127 | 0.9998 | 1.27 | -3862.25 | 180116.56 | Hochpunkt H(0.13|1) |
| 0.152 | 0.2915 | -41.39 | -1.72 | 85570.09 | Wendepunkt W(0.15|0.29) |
| 0.159 | 0.0061 | -39.55 | 487.59 | 50692.67 | Nullstelle N(0.16|0.01) |
| 0.212 | -1 | -0.1 | 496.03 | -13896.98 | Tiefpunkt T(0.21|-1) |
| 0.274 | -0.4865 | 11.64 | 1.37 | -2973.79 | Wendepunkt W(0.27|-0.49) |
| 0.318 | -0.0031 | 9.89 | -61.89 | -371.57 | Nullstelle N(0.32|0) |
| 0.5 | 0.9093 | 1.66 | -21.21 | 187.13 | |
| 0.636 | 1 | 0 | -6.12 | 57.44 | Hochpunkt H(0.64|1) |
| 0.928 | 0.8808 | -0.55 | 0 | 4.57 | Wendepunkt W(0.93|0.88) |
| 1 | 0.8415 | -0.54 | 0.24 | 2.34 | |
| 1.5 | 0.6184 | -0.35 | 0.34 | -0.37 | |
| 2 | 0.4794 | -0.22 | 0.19 | -0.23 | |
| 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