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最值问题是初中数学的一个重要内容,也是各种考试命题的一个热点。笔者根据自己的教学体会,将初中阶段所涉及的求函数最值问题的题目类型归纳如下。 一、求y=ax~2+bx+c(a≠0)型的最大(小) 值 当a>0时,y最小值=(4ac-b~2)/4a;当a<0时,y最大值=(4ac-b~2)/4a。 例1.求y=-2x+7的最大值. 解 ∵a<0,∴y最大值=(81)/8. 例2.求y=2x~2-3x+4的最小值. 解 ∵a<0,∴y最小值=(23)/8. 二、求隐二次函数的最大(小)值 已知y与x不成二次函数关系,但z与x成二次函数关系,可以先求z的最大(小)值,而后再求y的最大(小)值. 例3.求函数y=1/(2+(x-1)~2)的最大值.
The question of value is an important part of junior high school mathematics, and it is also a hot topic for various exam propositions. Based on my own teaching experience, the author summarizes the types of questions that are involved in the search for the most valued function in the junior high school stage. 1. Find the maximum (small) value of type y=ax~2+bx+c(a≠0). When a>0, the minimum value of y=(4ac-b~2)/4a; when a<0, y max = (4ac-b~2)/4a. Example 1. Find the maximum value of y=-2x+7. Solution ∵a<0, ∴y maximum value=(81)/8. Example 2. Find the minimum value of y=2x~2-3x+4. a<0, ∴y minimum=(23)/8. Second, find the maximum (small) value of the implicit quadratic function. Know that y and x do not have a quadratic function relationship, but z and x have a quadratic function relationship. First find the maximum (small) value of z, and then find the maximum (small) value of y. Example 3. Find the maximum value of the function y=1/(2+(x-1)~2).