已知函数f(x)=根号3cos4x-sin4x

问题描述:

已知函数f(x)=根号3cos4x-sin4x
已知函数f(x)=√3cos4x-sin4x
(1)求函数f(x)最小正周期;
(2)求函数f(x)在区间[-π/12,π/6]上的单调性及值域

f(x)=根号3cos4x-sin4x=2sin(4x+2π/3)
故T=π/2
(2)当x属于[-π/12,π/6]时,4x+2π/3属于[π/3,4π/3]
得到函数值域是[-√3,2]
令4x+2π/3=π/2得到x=-π/24
得到函数在[-π/12,-π/24]上递增,在[-π/24,π/6]上递减-2sin(4x-兀/3)=2sin(4x+2π/3)