Mathematics - Application of Derivative Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{f}(\mathrm{x})=4{\cos }^3(\mathrm{x})+3\sqrt{3}{\cos }^2(\mathrm{x})-10;\mathrm{x}\in (0,2\pi )\\ & \Rightarrow {\mathrm{f}}^{\prime }(\mathrm{x})=12{\cos }^2\mathrm{x}[-\sin (\mathrm{x})]+3\sqrt{3}(2\cos (\mathrm{x}))[-\sin (\mathrm{x})]\\ & \Rightarrow {\mathrm{f}}^{\prime }(\mathrm{x})=-6\sin (\mathrm{x})\cos (\mathrm{x})[2\cos (\mathrm{x})+\sqrt{3}]\end{array}$
local maxima at $\mathrm{x}=\frac{5\pi }{6},\frac{7\pi }{6}$