Bài tập 23 trang 227 SGK Toán 11 NC

a. Ta có:

\(\begin{array}{l}
y\prime  = \cos 2x + \cos x\\
y\prime  = 0 \Leftrightarrow \cos 2x + \cos x = 0\\
 \Leftrightarrow 2{\cos ^2}x + \cos x - 1 = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
\cos x =  - 1\\
\cos x = \frac{1}{2}
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = \pi  + k2\pi \\
x =  \pm \frac{\pi }{3} + k2\pi 
\end{array} \right.(k \in Z)
\end{array}\)

b.

\(\begin{array}{l}
y\prime  = 3\cos 3x + 6\sin 3x - 3\\
y\prime  = 0 \Leftrightarrow \cos 3x + 2\sin 3x = 1\\
 \Leftrightarrow \frac{1}{{\sqrt 5 }}\cos 3x + \frac{2}{{\sqrt 5 }}\sin 3x = \frac{1}{{\sqrt 5 }}\\
 \Leftrightarrow \cos (3x - \alpha ) = \cos \alpha \,\,(\cos \alpha  = \frac{1}{{\sqrt 5 }})\\
 \Leftrightarrow \left[ \begin{array}{l}
3x - \alpha  = \alpha  + k2\pi \\
3x - \alpha  =  - \alpha  + k2\pi 
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{2\alpha }}{3} + k\frac{{2\pi }}{3}\\
x = k\frac{{2\pi }}{3}
\end{array} \right.
\end{array}\)

-- Mod Toán 11 HỌC247