A

- Hướng dẫn giải

$$\begin{gathered} f\text{'}\left(x\right)=-5\sin \left(x\right)+5\sin \left(5x\right) \\ =10\cos \left(3x\right)\sin \left(2x\right) \\ f\text{'}\left(x\right)=0 \\ \iff \left\{\begin{array}{l}\sin \left(2x\right)=0\\ \cos \left(3x\right)=0\end{array}\right. \\ \iff \left\{\begin{array}{l}x=k\frac{\mathrm{\pi }}{2}\\ x=\frac{\mathrm{\pi }}{6}+k\frac{\mathrm{\pi }}{3}\end{array}\right. \end{gathered}$$

Do $x\in \left[-\frac{\mathrm{\pi }}{3};\frac{\mathrm{\pi }}{3}\right]$ nên $x\in \left\{-\frac{\mathrm{\pi }}{6};0;\frac{\mathrm{\pi }}{6}\right\}$ . Ta có

$$\begin{gathered} f\left(-\frac{\mathrm{\pi }}{3}\right)=f\left(\frac{\mathrm{\pi }}{3}\right)=2 \\ f\left(\frac{-\mathrm{\pi }}{6}\right)=f\left(\frac{\mathrm{\pi }}{6}\right)=3\sqrt{3} \\ f\left(0\right)=4 \end{gathered}$$

Suy ra M = $3\sqrt{3}$; m = 2. Vậy Mm = $6\sqrt{3}$

Đáp án A