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函数的最值问题广泛地联系着三角、几何、代数多方面的知识,又与生产实际中的问题密切联系在一起,是培养学生分析能力和综合运算能力的好课题.在实际教学过程中,借助函数的最值思想解题,有许多独到之处,也使问题的解决简便、快捷.一、直接求最值题目中的最值思想应用例1.设>0,y>0,若 x~/(1/2)+y~/(1/2)≤a(x+y)~/(1/2)恒成立,求 a 的最小值.解:由题知,不等式恒成立时 a>0,不等式等价于
The function of the function of the value of the most widely associated with the knowledge of triangles, geometry, algebra, and is closely linked with the problems in the actual production, is a good subject to cultivate students’ analytical ability and comprehensive computing ability. In the actual teaching process, Solving problems with the help of the function’s maximum value, there are a lot of unique features, but also to solve the problem is simple and fast. First, the value of the most direct value of the problem of thought Application Example 1. Set> 0, y> 0, if x ~/(1/2)+y~/(1/2)≤a(x+y)~/(1/2) is constant and finds the minimum value of a. Solution: From the inscription, when the inequality constant is established, a >0, inequality is equivalent to