Question

一道高中数学题!急!设函数f(x)=(x-1)＾2(x+b)e＾x,若x=1是f(x)的一个极大值,则实数b的取值范围是

Answer 1

f(x)=[(x-1)^2] [(x+b)] [e^x]

f '(x)=2(x-1) (x+b)[e^x] + [(x-1)^2] [(x+b)] [e^x] + [(x-1)^2] [e^x]

f ‘'(x)=2(x+b) [e^x] + 2(x-1) [e^x] + 2(x-1) (x+b) [e^x]

+ 2(x-1) (x+b)[e^x] + [(x-1)^2] [(x+b)] [e^x] + [(x-1)^2] [e^x]

+ 2(x-1) [e^x] + [(x-1)^2] [e^x]

因为x=1是f(x)的一个极大值,所以f ’'(1)