函数是高中数学的重点内容,在近年高考试卷中函数与数列、函数与不等式相结合的试题已成为热点问题,它经常作为压轴题出现。下面将重点讨论借用函数证明不等式问题。利用函数证明不等式,条件与结论之间跨度比较大,因此难度较大。这类题考查同学综合运用所学知识解决问题的能力。解决办法通常是利用函数的单调性,出现不等关系,借用该不等关系,寻求与所证明的目标不等式之间的联系,从而达到证明的目的。 The function is the key content of high school mathematics. In recent years, the test question that the combination of function and sequence, function and inequality has become a hot issue, and it often appears as a finale. The following will focus on borrowing function to prove the problem of inequality. Using function proved inequality, the span between conditions and conclusions is relatively large, so it is more difficult. This type of test examines students’ ability to use their knowledge to solve problems synthetically. The solution is to make use of the monotonicity of functions, unequal relations, to borrow the inequalities, and to seek the connection with the proved inequalities of objective so as to achieve the purpose of proof.