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借助函数来研究不等式问题是高考命题热点,构造出精准的辅助函数是解题的关键,而参考答案中的辅助函数是如何构造出来的呢?笔者对近三年湖北高考中的三道函数解答题进行了研究,试着用分析法分析问题来找出构造辅助函数的方法.例1(2012年湖北文)设函数f(x)=ax~n(1-x)+b(x>0),n为正整数,a,b为常数,曲线y=f(x)在(1,f(1))处的切线方程为x+y=1.
With the function to study inequality is the hot topic of college entrance examination, construct a precise auxiliary function is the key to solving the problem, and reference answers in the auxiliary function is constructed out of the author of the last three years Hubei college entrance examination in the three functions to answer Try to find the way to construct the auxiliary function by analyzing the problem.Example 1 (Hubei Province, 2012) Let f (x) = ax ~ n (1-x) + b (x> 0) , n is a positive integer, a and b are constants, and the curve y = f (x) has the tangent equation at (1, f (1)) as x + y = 1.