$$\begin{aligned} & f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10 \\ & f^{\prime}(x)=12 \cos ^2 x \cdot(-\sin x)+6 \sqrt{3} \cos x \cdot(-\sin x)=0 \\ & =-6 \sqrt{3} \cos x \cdot \sin x\left(1+\frac{2}{\sqrt{3}} \cos x\right)=0 \\ & \cos x=0, \sin x=0, \cos x=\frac{-\sqrt{3}}{2} \end{aligned}$$

Sign of $$f(x)$$

$$\therefore \text { Maxima at } \frac{5 \pi}{6}, \frac{7 \pi}{6}$$