函数极值和最值间的区别与联系

The difference and relation between the condition extremum and the condition maximum

在实际问题中,常常会遇到为了发挥最大的经济效益,要求在一定的条件下,提高生产效率,降低成本,节约原料,以达到利润最大化,费用最省;或施工中受污染程度最小等问题。解决这类问题就需要用到函数的极值和最值的知识。而这两个概念非常接近,学生在学习过程中经常混淆,区分不开。本文深入分析函数的极值与最值概念间的区别与联系,以及求解极值与最值的步骤,从而找出学生易于理解的方法。

In the actual problem, often encountered in order to maximize the economic benefit, under certain conditions, improve the production efficiency, reduce costs, save raw materials, to achieve the profit maximization, cost of the province; Or the minimum pollution level of the construction. Solving these problems requires the use of the extremum and the best knowledge of the function. These two concepts are very close to each other, and students are often confused during the learning process. In this paper, the difference and relationship between the extreme value of the function and the most value concept are analyzed in this paper, as well as the steps to solve the extremum and the most value, so as to find out the method which the students can understand easily.