Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 2 / 18 / a / Solution

Differentiating givesThe exponential never vanishes, so all stationary points have $x=k\pi /2$. At $x=k\pi$, $y=1$ and $y^{\prime \prime }=2>0$; at $x=\pi /2+k\pi$, $y=e$ and $y^{\prime \prime }=-2e<0$. ThusThese are global minima and maxima because $0\le {\sin }^{2}x\le 1$. None of the stationary points is an inflection point.