Editing Derivative test (section)

==Multivariable case==
{{Main article|Second partial derivative test}}
For a function of more than one variable, the second-derivative test generalizes to a test based on the [[eigenvalue]]s of the function's [[Hessian matrix]] at the critical point. In particular, assuming that all second-order partial derivatives of ''f'' are continuous on a [[neighbourhood (mathematics)|neighbourhood]] of a critical point ''x'', then if the eigenvalues of the Hessian at ''x'' are all positive, then ''x'' is a local minimum. If the eigenvalues are all negative, then ''x'' is a local maximum, and if some are positive and some negative, then the point is a [[saddle point]]. If the Hessian matrix is [[singular matrix|singular]], then the second-derivative test is inconclusive.