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.