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近几年的高考出现了与函数不等式有关的压轴题.此类题往往由常见函数的单调性和常用不等式引伸出来,如果不了解试题的背景,将导致论证上的困难或证明复杂化.为理清解题思路、简化解题过程,本文重点探究f(x)>g(x)与f’(x)>g’(x)的联系,以供参考.全文假设f(x)、g(x)在[a,b]上连续,在(a,b)上可导,令F(x)=f(x)-g(x).
In recent years, college entrance examination appeared with the function inequality-related finale problem.This kind of problem is often drawn by the monotonicity of common functions and common inequalities, if you do not understand the background of the questions, will lead to the difficulty of argumentation or prove complicated. To clarify the problem-solving ideas and simplify the problem-solving process, this paper focuses on the relationship between f (x)> g (x) and f ’(x)> g (x) is continuous on [a, b] and is guided on (a, b) such that F (x) = f (x) -g (x).