Question

求函数y=(x-1)e^arctanx 的单调区间及极值

Answer 1

y=(x-1)e^arctanx

y'=e^arctanx+(x-1)e^arctanx*1/(1+x^2)

=e^arctanx[(1+x^2)+(x-1)]/(x^2+1)

=e^arctanx(x^2+x)/(x^2+1)=0

∵e^arctanx>0

(x^2+1)>0

∴x^2+x=0

x(x+1)=0

所以当x>0或x