y'=e^arctanx/(x^2+1)
y"
=[e^arctanx*(x^2+1)/(x^2+1)+e^arctanx*2x]/(x^2+1)^2
=e^arctanx*(1+2x)/(x^2+1)^2
y"=0得到x=-1/2
在x<-1/2時(shí)y"<0,函數(shù)y為凸函數(shù)
在x>-1/2時(shí)y">0,函數(shù)y為凹函數(shù)
x=-1/2時(shí)y=e^[-arctan(1/2)]
凸區(qū)間為(-無窮,-1/2)
凹區(qū)間為(-1/2,+無窮)
拐點(diǎn)(-1/2,e^[-arctan(1/2)])