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在最近几年的高考试卷中,经常出现以e~x或lnx与一个多项式的和、差、积或商为背景函数解析式,以应用导数研究函数为主要考查方法,涉及切线、单调性、最值(极值)、方程、不等式、字母参数等内容,综合考查转化与划归、函数与方程、分类讨论、数形结合等思想的问题.2013年江苏卷的第20题就是这样的问题:原题:设函数f(x)=lnx-ax,g(x)=e~x-ax,其中a为实数.(1)若f(x)在(1,+∞)上单调递减,且g(x)在(1,+∞)上有最小值,试求a的取值范围;
In the college entrance examination papers in recent years, the analytic expression of the sum, difference, product or quotient of e ~ x or lnx and a polynomial often appears in the college entrance examination papers. The application of the function of derivative research as the main examination method involves the tangential, monotonic, The most value (extreme value), the equation, the inequality, the alphabetic parameter and so on, examines the conversion and the classification, the function and the equation, the classification discussion, the digit combination and so on thought question. (1) If f (x) decreases monotonically on (1, + ∞), then f (x) = lnx- And g (x) has the minimum value on (1, + ∞)