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在各种练习及考试中,常见到这样问题“……恒为正数(负数)”,“……恒有解”,“……恒成立”。如何处理这一类问题呢?本文不揣浅陋,谈谈自己的看法,以就教于同仁。例1 已知函数f(x)=(x-1)log_4~2k-6xlog_4k+x+1在区间[0,1]上恒为正值,求实数k的取值范围。分析:欲使函数f(x)在某区间恒为正值,我们只要求f(x)在此区间的最小值为正值即可,这样问题就转化为求函数f(x)最小值。解∵f(x)=(log_4~2k-6log_4~2k+1)x+(1-
In various exercises and examinations, such questions as “... constant positive numbers (negative numbers)”, “... constant solutions”, “... constant establishment”. How to deal with this kind of problem? This article is not very shy, talk about their own views, so as to teach in my colleagues. Example 1 It is known that the function f(x)=(x-1)log_4~2k-6xlog_4k+x+1 is always positive in the interval [0,1], and the range of the real number k is obtained. Analysis: To make the function f(x) constant in a certain interval, we only require that the minimum value of f(x) in this interval be a positive value, and the problem is then converted into the minimum value of the function f(x). Solution f(x)=(log_4~2k-6log_4~2k+1)x+(1-