At present, we in the scientific production often extreme value of function are discussed, but we are very familiar with the elementary method to solve the function of finite element, in the face of many function if we use the elementary method to solve will become very hard or even impossible to solve, so, this paper introduced from about several aspects: definition two extreme value of binary function and the presence of a two order conditions, extreme value of binary function partial derivative method; method of conditional extreme value and application; n value of binary function definition and existing conditions and problems, n function repeated extreme, vector method for solving a class of multivariate function extreme value. Through the above method is introduced, aiming for future study and work to bring certain convenience.