The paper provides an entire derivation of necessary conditions represented by determinant for conditional extreme value of multivariate function , binary function and ternary function under the equality constraints . And geometrical interpretations are presented to explain the necessary conditions for conditional extreme value of binary , ternary function .These necessary conditions simplify the solution of the constrained extreme value problem as they avoid the interference of Lagrange multiplicator in solving the final equation .%推导证明了一般 n元函数及常用的二元、三元函数在等式约束条件下用行列式表示的极值的必要条件 ,并从几何上对二元、三元函数在等式约束条件下取极值的必要条件予以了直观解释 .利用这些必要条件求解条件极值 ,因除去了Lagrange乘数法带来的Lagrange乘子对解方程组的困扰 ,而使得最终方程组的求解变得明快简洁 .
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