n. a test for the optimality of a critical point of a function that uses second-order information. Thus, for a function of one variable one checks whether the second derivative at the point is positive (a local minimum) or negative (a local maximum) or zero (indeterminate). For a function of several variables one checks whether the Hessian at the point is positive definite (a local minimum) or negative definite (a local maximum), indefinite (a saddle point), or singular (indeterminate); if the determinant of the Hessian at the point is negative the point is a saddle point. Compare first derivative test.