Second derivative test

The second derivative test is used to determine whether a function has a relative minimum or maximum at a critical point. A critical point is a point at which the first derivative of a function, f'(x), equals 0. It can also be used to test the concavity of a function and potentially identify inflection points (points where the curve changes from being concave down to concave up, or vice versa).

The second derivative is often denoted as f''(x), where the first derivative is denoted as f'(x).

Testing for extrema

Testing for concavity

See also first derivative test, derivatives.