Editing Mathematical optimization (section)

=== Sufficient conditions for optimality ===
While the first derivative test identifies points that might be extrema, this test does not distinguish a point that is a minimum from one that is a maximum or one that is neither. When the objective function is twice differentiable, these cases can be distinguished by checking the second derivative or the matrix of second derivatives (called the [[Hessian matrix]]) in unconstrained problems, or the matrix of second derivatives of the objective function and the constraints called the [[Hessian matrix#Bordered Hessian|bordered Hessian]] in constrained problems. The conditions that distinguish maxima, or minima, from other stationary points are called 'second-order conditions' (see '[[Second derivative test]]'). If a candidate solution satisfies the first-order conditions, then the satisfaction of the second-order conditions as well is sufficient to establish at least local optimality.