Fermat Stationary Point Criterion

Let $I$ be an interval in the sense of Interval in the Real Line, let $f:I\to\mathbb{R}$, let $c\in I$ be an Interior Point of an Interval, and assume that $f$ is differentiable at $c$ in the sense of Derivative of a Real Function on an Interval. If $f$ has a local extremum at $c$ in the sense of Local Extremum at a Point, then

$$f'(c)=0.$$