求曲线的凹凸区间和拐点
问题描述：
求曲线的凹凸区间和拐点
求曲线y=e^arctanx的凹凸区间和拐点
答
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在x>-1/2时y">0,函数y为凹函数
x=-1/2时y=e^[-arctan(1/2)]
凸区间为(-无穷,-1/2)
凹区间为(-1/2,+无穷)
拐点(-1/2,e^[-arctan(1/2)])