Interior Extremum Theorem

The interior extremum theorem, also known as Fermat's theorem after the French mathematician Pierre de Fermat, states that any local extremum of a real function at a point where the function is differentiable must be a stationary point, meaning its derivative is zero there. The theorem gives a necessary but not sufficient condition for a local extremum, since some stationary points are not extrema, and while the second derivative can help distinguish a maximum from a minimum, it can also vanish at a genuine extremum. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/