关于二元函数极值的两个注记

Two Notes on Extreme Value of Functions of Two Variables

求二元函数极值,通常是利用函数对的二阶偏导数来展开。本文给出根据函数对的二阶偏导数来求解的方法。先对常规的二元函数极值求解方法做出评述,再证明可利用函数对的二阶偏导数求出极值,并举例加以进一步论证;求二元函数条件极值时,需注意区分目标函数与条件函数。上述两个重要注记不仅对教学有所帮助,而且对于实际生活、特别是经济实践中的最优化设计和计算,以及丰富完善相关的理论,都有一定的参考价值。

In order to find the extreme value of the functions of two variables,the second-order partial derivative of function is usually used with respect to x.In this paper,a method is given to solve the problem by utilizing the second-order partial derivative of function with respect to y.In the beginning,the paper reviews the conventional methods of solving the extreme value of binary function,and then proves that the extreme value can be obtained by using the second-order partial derivative of function with respect to y.When finding the conditional extreme value of binary function,attention should be paid to discriminating the objective function from the conditional function.The two important notes above are not only helpful to the teaching process,but also benefit the optimization design and calculation in daily life as well as the enrichment and improvement of relevant theories.