已知函数f(x)=4cosxcos(x-派/3)-2 1、求fx的最小正周期及单调递增区间 2 .

Question

已知函数f(x)=4cosxcos(x-派/3)-2
1、求fx的最小正周期及单调递增区间
2 .求函数fx在区间【-派/4,派/4】上的最大值和最小值

Answer 1

f(x)=4cosxcos(x-π/3)-2

=4cosx[1/2cosx+√3/2sinx]-2
=2cos^2x+2√3sinxcosx-2
=√3sin2x+cos2x-1
=2sin(2x+π/6)-1
T=2π/2=π
2x+π/6在[2kπ-π/2,2kπ+π/2]单调递增

x在[kπ-π/3,kπ+π/6]单调递增
2)x在[-π/4,π/4]
2x+π/6在[-π/3,2π/3]
最大值=1
最小值=-1-√3