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在高中数学中,我们经常会遇到求取值范围或者求最值(最大值和最小值)的问题,对于这类题目大的方向可以往函数(构造函数然后利用基本初等函数的性质或者导数研究其单调性,根据单调性找范围)或者不等式(基本不等式最重要的应用就是求最值),下面通过一个具体问题来阐述自己的一些想法。题目:x,y满足x2+2xy+4y2=6,求z=x+4y2的取值范围。我首先给出几种该问题的解题方法:方法一:∵x2+2xy+4y2=6,∴x2+4y2=6-2xy≥2·x·2y,由此可得
In high school mathematics, we often encounter the problem of finding a range of values or finding the maximum (maximum and minimum) for which large direction can be passed to the function (the constructor then takes advantage of the nature of the elementary elementary functions or derivatives Study its monotony, according to monotonicity to find the range) or inequality (the most important application of basic inequalities is to find the most value), the following through a specific question to explain some of their own ideas. Title: x, y satisfy x2 + 2xy + 4y2 = 6, Find z = x + 4y2 range of values. First of all, I will give you some solutions to this problem: Method 1: ∵x2 + 2xy + 4y2 = 6, ∴x2 + 4y2 = 6-2xy≥2 · x · 2y,