Critical point

Critical points are the only points at which extrema of a function can be found.[cite:@boelkins2025active] The critical points of differentiable functions mark the "turning points" of curves, where the derivative changes sign.

Definition

A member $c$ of a function $f$'s domain is called a critical number if $f^{\prime }c=0$ or if $f^{\prime }c$ is undefined.