In calculus, a branch of mathematics, the **second derivative test** determines whether a given stationary point of a function is a maximum or a minimum.

The test states: If the function *f* is twice differentiable in a neighbourhood of a stationary point *x*, then:

- If
*f*''(*x*) < 0 then*f*has a maximum at*x*. - If
*f*''(*x*) > 0 then*f*has a minimum at*x*.

Note that if *f*''(*x*) = 0 the second derivative test says nothing about the point *x*.