在学习向量的过程中,有如下两个结论:a·b≤|a·b|≤|a|·|b|;|a|-|b|≤|a+b|≤|a|+|b|.本文旨在通过一些例子说明,有针对性地、恰当地构造向量,运用上述结论,能简明快捷地探求四类无理函数的最值.1.f(x)=λx+m+μn-x(m+n0,λ0,μ0)型例1求函数y=2 3x+6+5 28-2x的最大值.解 In the process of learning vector, we have the following two conclusions: a · b ≤ a b ≤ ≤ a b · b a ≤ b | ≤ | a + b | ≤ | a | + | b |. The purpose of this paper is to illustrate some of the examples and to construct vectors in a pertinent and appropriate way. Using the above conclusions, we can find the most value of the four types of irrational functions in a concise and expeditious manner.1. f (x) = λx + m + μn -x (m + n0, λ0, μ0) Example 1 Find the maximum of the function y = 2 3x + 6 + 5 28-2x. Solution