MathNet 2017-part-04 — 176 problems (EN–VI) Question 92

Let $f(x) = \sqrt{4 \sin^4 x - \sin^2 x \cos^2 x + 4 \cos^4 x}$ for any $x \in \mathbb{R}$. Let $M$ and $m$ be the maximum and minimum values of $f$, respectively. Find the product of $M$ and $m$.