函数f(x)=sin2x+cos2x在区间(0,π/2)上取极大值时,x=?
问题描述:
函数f(x)=sin2x+cos2x在区间(0,π/2)上取极大值时,x=?
答
f(x)=sin2x+cos2x=根号2xsin(2x+π/4),2x+π/4在区间(π/4,5π/4)上,当f(x)取极大值时,2x+π/4=π/2,得x=π/8
函数f(x)=sin2x+cos2x在区间(0,π/2)上取极大值时,x=?
f(x)=sin2x+cos2x=根号2xsin(2x+π/4),2x+π/4在区间(π/4,5π/4)上,当f(x)取极大值时,2x+π/4=π/2,得x=π/8