Cho hàm số \(g\left( t \right) = {\sin ^2}2t\). Tính \(g''\left( {\frac{\pi }{8}} \right),g''\left( {\frac{\pi }{{12}}} \right)\)
A. 0; 4 | B. 1; 4 | C.1; 2 | D. 3; 1 |
\(g\left( t \right) = {\sin ^2}2t = \frac{{1 - \cos 4t}}{2}\)
Suy ra
\(\begin{array}{l}
g'\left( t \right) = - \frac{1}{2}.\left( { - 4\sin 4t} \right) = 2\sin 4t\\
g''\left( t \right) = 8\cos 4t
\end{array}\)
Do đó:
\(\begin{array}{l}
g''\left( {\frac{\pi }{8}} \right) = 8.cos\left( {4.\frac{\pi }{8}} \right) = 0;\\
g''\left( {\frac{\pi }{{12}}} \right) = 8.\cos \left( {4.\frac{\pi }{{12}}} \right) = 8.\cos \frac{\pi }{3} = 4
\end{array}\)
Chọn A.
-- Mod Toán 11