If $f(x)=\left|\begin{array}{ccc}\cos (2 x) & \cos (2 x) & \sin (2 x) \\ -\cos x & \cos x & -\sin x \\ \sin x & \sin x & \cos x\end{array}\right|$, then
Select ALL correct options:
A
$f(x)$ attains its maximum at $x=0$
B
$\mathrm{f}(\mathrm{x})$ attains its mininum at $\mathrm{x}=0$
C
$f^{\prime}(x)=0$ at exactly three points in $(-\pi, \pi)$
D
$f^{\prime}(x)=0$ at more than three points in $(-\pi, \pi)$
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