利用二阶方向导数证明极值的充分条件

Second Order Directional Derivatives and the Second Partial Derivative Test

介绍二元函数二阶方向导数的概念与计算方法.利用线性代数中的二次型知识,对二元函数在驻点处是否取得极值的充分性定理给出有几何意义的证明.

This paper introduces the second order directional derivative and the formula for computing it. By using second order directional derivative and quadratic forms, a proof of the second partial derivative test for two-variable functions is provided, which has direct geometrical interpretation.