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Funktion: f(x) = 2·sin(3x)/x, Df = R\{0}, Wf = [-1.3034;6), reelle Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0 ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -7 | 0.239 | 0.5 | -2.01 | -5.07 | |
| -6.7925 | 0.2942 | 0.01 | -2.65 | -0.8 | Hochpunkt H(-6.79|0.29) |
| -6.5 | 0.1863 | -0.71 | -1.89 | 5.76 | |
| -6.285 | 0.0017 | -0.95 | -0.32 | 8.45 | Nullstelle N(-6.28|0) |
| -6.25 | -0.0318 | -0.96 | -0.02 | 8.59 | Wendepunkt W(-6.25|-0.03) |
| -6 | -0.2503 | -0.7 | 2.02 | 6.93 | |
| -5.7425 | -0.3478 | -0.01 | 3.13 | 1.12 | Tiefpunkt T(-5.74|-0.35) |
| -5.5 | -0.2588 | 0.72 | 2.59 | -5.51 | |
| -5.2375 | -0.0017 | 1.15 | 0.45 | -10.06 | Nullstelle N(-5.24|0) |
| -5.195 | 0.0472 | 1.16 | 0.02 | -10.31 | Wendepunkt W(-5.19|0.05) |
| -5 | 0.2601 | 0.96 | -1.96 | -9.36 | |
| -4.69 | 0.4255 | 0 | -3.83 | -1.63 | Hochpunkt H(-4.69|0.43) |
| -4.5 | 0.3572 | -0.71 | -3.53 | 4.83 | |
| -4.19 | 0.0017 | -1.43 | -0.7 | 12.4 | Nullstelle N(-4.19|0) |
| -4.135 | -0.0777 | -1.45 | 0 | 12.9 | Wendepunkt W(-4.13|-0.08) |
| -4 | -0.2683 | -1.33 | 1.75 | 12.69 | |
| -3.635 | -0.548 | 0 | 4.93 | 2.67 | Tiefpunkt T(-3.63|-0.55) |
| -3.5 | -0.5027 | 0.67 | 4.91 | -3.19 | |
| -3.1425 | -0.0017 | 1.91 | 1.23 | -16.03 | Nullstelle N(-3.14|0) |
| -3.07 | 0.1388 | 1.95 | 0.02 | -17.18 | Wendepunkt W(-3.07|0.14) |
| -3 | 0.2747 | 1.91 | -1.2 | -17.6 | |
| -2.5775 | 0.7702 | 0.02 | -6.92 | -5.45 | Hochpunkt H(-2.58|0.77) |
| -2.5 | 0.7504 | -0.53 | -7.18 | -1.05 | |
| -2.095 | 0.0017 | -2.86 | -2.75 | 21.89 | Nullstelle N(-2.1|0) |
| -2 | -0.2794 | -3.02 | -0.51 | 25.2 | |
| -1.9825 | -0.3323 | -3.03 | -0.06 | 25.66 | Wendepunkt W(-1.98|-0.33) |
| -1.5 | -1.3034 | -0.03 | 11.7 | 15.72 | Tiefpunkt T(-1.5|-1.3) |
| -1.0475 | -0.0017 | 5.73 | 10.95 | -20.29 | Nullstelle N(-1.05|0) |
| -1 | 0.2822 | 6.22 | 9.9 | -23.84 | |
| -0.695 | 2.5056 | 7.85 | 0.04 | -38.05 | Wendepunkt W(-0.69|2.51) |
| -0.5 | 3.99 | 7.13 | -7.39 | -36.63 | |
| 0 | - | - | - | - | Lücke L(0|6) |
| 0.5 | 3.99 | -7.13 | -7.39 | 36.71 | |
| 0.6925 | 2.5252 | -7.85 | -0.05 | 38.05 | Wendepunkt W(0.69|2.53) |
| 1 | 0.2822 | -6.22 | 9.9 | 23.66 | |
| 1.045 | 0.0126 | -5.75 | 10.9 | 20.29 | Nullstelle N(1.05|0.01) |
| 1.4975 | -1.3034 | 0 | 11.74 | -15.72 | Tiefpunkt T(1.5|-1.3) |
| 1.5 | -1.3034 | 0.03 | 11.7 | -15.88 | |
| 1.98 | -0.3399 | 3.03 | 0 | -25.66 | Wendepunkt W(1.98|-0.34) |
| 2 | -0.2794 | 3.02 | -0.51 | -25.13 | |
| 2.0925 | -0.0054 | 2.87 | -2.69 | -21.89 | Nullstelle N(2.09|-0.01) |
| 2.5 | 0.7504 | 0.53 | -7.18 | 1.2 | |
| 2.575 | 0.7702 | 0 | -6.93 | 5.45 | Hochpunkt H(2.58|0.77) |
| 3 | 0.2747 | -1.91 | -1.2 | 17.6 | |
| 3.0675 | 0.1437 | -1.95 | -0.02 | 17.18 | Wendepunkt W(3.07|0.14) |
| 3.14 | 0.003 | -1.91 | 1.19 | 16.03 | Nullstelle N(3.14|0) |
| 3.5 | -0.5027 | -0.67 | 4.91 | 3.07 | |
| 3.6325 | -0.5479 | -0.01 | 4.94 | -2.67 | Tiefpunkt T(3.63|-0.55) |
| 4 | -0.2683 | 1.33 | 1.75 | -12.71 | |
| 4.1325 | -0.0813 | 1.45 | 0.03 | -12.9 | Wendepunkt W(4.13|-0.08) |
| 4.1875 | -0.0018 | 1.43 | -0.67 | -12.4 | Nullstelle N(4.19|0) |
| 4.5 | 0.3572 | 0.71 | -3.53 | -4.74 | |
| 4.6875 | 0.4255 | 0 | -3.83 | 1.63 | Hochpunkt H(4.69|0.43) |
| 5 | 0.2601 | -0.96 | -1.96 | 9.39 | |
| 5.1925 | 0.0501 | -1.16 | -0.01 | 10.31 | Wendepunkt W(5.19|0.05) |
| 5.235 | 0.0011 | -1.15 | 0.43 | 10.06 | Nullstelle N(5.24|0) |
| 5.5 | -0.2588 | -0.72 | 2.59 | 5.45 | |
| 5.74 | -0.3478 | 0 | 3.13 | -1.12 | Tiefpunkt T(5.74|-0.35) |
| 6 | -0.2503 | 0.7 | 2.02 | -6.97 | |
| 6.2475 | -0.0342 | 0.96 | 0 | -8.59 | Wendepunkt W(6.25|-0.03) |
| 6.2825 | -0.0007 | 0.96 | -0.3 | -8.45 | Nullstelle N(6.28|0) |
| 6.5 | 0.1863 | 0.71 | -1.89 | -5.71 | |
| 6.79 | 0.2942 | 0 | -2.65 | 0.8 | Hochpunkt H(6.79|0.29) |
| 7 | 0.239 | -0.5 | -2.01 | 5.11 | |
| 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