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已知f(x,y)=0,求g(x,y)的最值,这是高中数学新教材中常见的一类“条件最值”题.这类题在高考中常出现,其解法由于教材中没有系统论述,且思维灵活性较强,同学们往往难以入手.本文试通过一道课本习题,多层面探究其解法,并总结出解这类题的若干数学思想,然后通过相关习题运用数学思想,体验“最值”解法,以达到灵活应用的目的. 一、一题多解,体现数学思想例1已知x2+y2=16,求x+y的最大值和最小值.(选自人教版全日制普通高级中学教科书(必修)数学第二册(上)P89第6题)
Knowing f(x,y) = 0, find the maximum value of g(x,y), which is a common “highest condition” question in new mathematics textbooks for high schools. Such questions often appear in college entrance examinations, and their solutions Because there is no systematic discussion in the teaching material and the thinking flexibility is relatively strong, the students are often difficult to get started. This article tries to adopt a textbook exercise to explore its solution in multiple layers, and summarizes a number of mathematical ideas for solving such problems, and then applies the relevant exercises. Mathematical thinking, to experience the “value” solution, in order to achieve the purpose of flexible application. One, multiple solutions to the problem, reflecting the mathematical thinking example 1 is known x2 + y2 = 16, find the maximum and minimum x + y. (Select Self-educated edition Full-time Ordinary High School Textbook (Required) Math Volume 2 (on) P89 Question 6)