We can often determine if a stationary point is a local minimizer or maximizer using a more direct test on the curvature of the function. Remark 4. If x is a stationary point of f : R R and f"(x) > 0 ("(x) < 0), then x is a local minimizer (maximizer) of f. This last remark is an example of what mathematicians call a sufficient condition. If the condition is met then it is a sufficient test to establish the conclusion. However, it is not a necessary condition because the conclusion may be true even if the test fails. In this case we have the following result. Remark 5. If x is a stationary point of f : R R and f"(x) = 0, then x may be a local minimizer, a local maximizer, neither or both.