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近几年,有好多高中生问一些函数最小值的求解问题,笔者把这些函数进行了归纳,是一类函数f(x)=((x-a)~2+b~2)~(1/2)+((x-c)~2+d~2)~(1/2)(b>0,d>0).因为f(x)不但是无理式,而且是两个无理式的和,这对一部分高中生来说,求f(x)的最小值有一些难度.下面提供几种解法仅供参考,而且从方法论层面梳理了一下各种解法之间的关联,供高中生学习数学参考.1四种不同解法
In recent years, there are a lot of high school students asking some questions about the minimum function. The author has summarized these functions and it is a kind of function f(x)=((xa)~2+b~2)~(1/2 )+((xc)~2+d~2)~(1/2)(b>0,d>0). Since f(x) is not only an irrational formula, but also a sum of two irrational formulas, For some high school students, there are some difficulties in finding the minimum value of f(x). The following solutions are provided for reference only, and the association between various solutions is combed from a methodological perspective for high school students to learn mathematics reference. 1 Different solutions