浅谈洛必达法则在导数大题中的应用

On the Application of L'Hospital's rule in Derivative Problems

纵观近些年高考真题,导数在卷末压轴大题中的出题频率居高不下。通过调查与访谈,发现高三学生对压轴大题的最后一问普遍感到棘手,尤其是对求参数取值范围的这种经典题目。在高中教师通常会以分类讨论的方式对求参数的取值范围这种导数经典题目进行讲解。通过分离变量法,用洛必达法则对这种参数比较好分离的情况进行分析,希望能够为高中生求解这种问题提供新的思路。

Throughout the real questions of college entrance examination in recent years,the frequency of derivatives in the big questions at the end of the paper is high.Through the investigation and interview,it is found that senior three students are generally difficult to solve the last question of the final question,especially for the classic topic of finding the range of parameter values.In senior high school,teachers usually explain the derivative classic topic of finding the value range of parameters in the way of classified discussion.Through the method of separating variables and the law of L’Hospital’s rule,this paper analyzes the better separation of the parameters,hoping to provide new ideas for senior high school students to solve this problem.