Question:

Let $f(x)=4\cos^3 x+3\sqrt{3}\cos^2 x-10$. The number of points of local maxima of $f$ in the interval $(0,2\pi)$ is:

Step-by-Step Solution

Key Concept: $f'(x)=-6\sin x\cos x(2\cos x+\sqrt{3})=0$. Local maxima at $x=5\pi/6$ and $7\pi/6$.

2 local maxima.

Correct Answer: 4