Second Derivative Test

Let $f$ be a twice differentiable function on an open interval containing $c,$ and further let $f'(c)=0.$

• If $f''(c)>0,$ then $f(c)$ is a relative minimum of $f.$
• If $f''(c)<0,$ then $f(c)$ is a relative maximum of $f.$
• If $f''(c)=0,$ then the test is inconclusive (use the First Derivative Test.)