n. a test for optimality of a critical point of a given function using only the first derivative: the critical point c is a local minimum if in some neighborhood of c the derivative f'(x) is strictly positive to the left of c and strictly negative to its right; it is a local maximum if the derivative is strictly negative to the left and strictly positive to the right of c. For example, A is a local maximum and B is a local minimum; the change of derivative from positive at X to negative at Y, and thence to positive at Z, is shown by the tangents at these points. Compare second derivative test, point of inflection.