Question

已知函数f(x)=√3cos

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

Answer 1

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