Fermat's stationary-point theorem

Let \(a<b\), let \(f\colon[a,b]\to\RR\), and let \(c\in(a,b)\). If \(f\) has a local maximum or a local minimum at \(c\) and \(f\) is differentiable at \(c\), then \(f'(c)=0\). [@Rud76].