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值域(最值)问题是历年高考的必考知识点,对于一元函数的值域(最值)问题的处理方法有很多种,如:单调性法、分离常数法、判别式法、换元法(代数换元、三角换元)、导数法等等.但是针对二元的值域(最值)问题有时可以利用消元转化为一元问题,也可以用线性规划知识,还可以利用重要不等式(如柯西不等式)等方法.下面以一道有关二元的值域问题为例,从五个不同角度对其进行求解,从而对类似问题作一个归纳总结,希望能抛砖引玉!
The problem of value range (the most value) is the compulsory knowledge of the college entrance examination in the past years. There are many ways to deal with the range (the most value) problem of a unitary function, such as the monotonicity method, the separation constant method, the discriminant method, (Algebraic transformation, trigonometric transformation), derivative method, etc. However, the problem of binary range (most value) can sometimes be transformed into a unary problem using elimination, linear programming knowledge can also be used, you can also use the important inequalities (Such as Cauchy inequality), etc. Below a binary value range problem, for example, from five different angles to solve them, so as to make a summary of similar problems, hoping to start a discussion!