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Gaokao Math Practice Question

已知函数 $f(x)=\cos x \sin 2 x$, 下列结论中不正确的是 ($\qquad$)

  1. A.$y=f(x)$ 的图象关于 $(\pi, 0)$ 中心对称
  2. B.$y=f(x)$ 的图象关于 $x=\frac{\pi}{2}$ 对称
  3. C.$f(x)$ 的最大值为 $\frac{\sqrt{3}}{2}$
  4. D.$f(x)$ 既是奇函数, 又是周期函数

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