1题目呈现已知函数f(x)=ax~2-e~x(a∈R),f′(x)是f(x)的导函数。(e为自然对数的底数)(Ⅰ)解关于x不等式:f(x)>f′(x);(Ⅱ)若f(x)有两个极值点x_1、x_2,求实数a的取值范围。笔者在课堂检测中发现,学生解答第(工)问的正确率比较高,但第(Ⅱ)问全班有一半以上的学生解答出错,更有思维受阻者,不会解答。能够解答的学生多数是利用导数求极值的方法,只有少数学生是将函数零点转化为方程的根,依据方程重新构造两个函 1 The topic presents the known function f (x) = ax ~ 2 -e ~ x (a∈R), f ’(x) is the derivative of f (x). (e is the base of the natural logarithm) (Ⅰ) Solve x inequality: f (x)> f ’(x); (Ⅱ) If f (x) has two extremum points x_1 and x_2, find the real a Ranges. In the classroom test, the author found that the correct answer rate of students’ answers to the (Part I) questions was relatively high. However, question (II) asked more than half of the students in the entire class to answer wrongly and even thought-impaired people would not answer them. Most of the students who can answer are using the method of deriving the extremum of the derivative. Only a few students transform the zero point of the function into the root of the equation and reconstruct two letters according to the equation