First Derivative Test

Let $f$ be a continuous function on an open interval $I$ containing $c,$ and further let $c$ be a critical number of $f.$ If $f$ is differentiable on $I$ except possibly at $c,$ then:

• if the sign of $f'(x)$ changes from negative to positive at $c,$ then $f(c)$ is a relative minimum of $f.$
• if the sign of $f'(x)$ changes from positive to negative at $c,$ then $f(c)$ is a relative maximum of $f.$