Second derivative test

In calculus, the second derivative test is a tactic used to determine if a local extremum occurs at a given critical point of a twice-differentiable function.

Statement

Let $a$ be a critical point. If $f^{\prime \prime }a<0$, then there is a local maximum at $a$. If $f^{\prime \prime }a>0$, it is a local minimum.

See also

• First derivative test