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一、问题的由来笔者注意到2012年合肥市第二次质量检测试题文科数学第21题是一道关于函数导数的题,解决时运用了函数图象,但是该题函数图象并不是每个考生都能画出来的。1.问题再现设函数f(x)=(x2-2x+a+2)ex(x∈R)(1)若a=-1,求f(x)在[0,2]上的最大值与最小值;(2)过点(-1,0)作曲线y=f(x)的切线,如果有三条,求a的取值范围。2.问题解答
First, the origin of the problem I noticed that the second quality test in Hefei in 2012 Liberal Arts Mathematics Problem 21 is a question on the function of the derivative, the use of the function to solve the image, but the problem function image is not every candidate Can draw it out. 1. Reproduce the function f (x) = (x2-2x + a + 2) ex (x∈R) (1) If a = -1, find the maximum value of f And the minimum value; (2) point (-1,0) for the curve y = f (x) tangent, if there are three, find the range of a. 2. Questions and answers