Question

已知f（x）=—4cos平方x+4根号3 sinxcosx+5 x属于R 1）求f（x)取得最大值时x的集合 2）求f（

Answer 1

f（x）=—4cos平方x+4根号3 sinxcosx+5=-4*(cos2x+1)/2+2√3sin2x+5

=4(sin2x*√3/2-cos2x*1/2)+3=4sin(2x-π/6)+3

当f(x)取最大值4+3=7时解的集合为2x-π/6=2kπ+π/2,得x=kπ+π/3,k∈Z

f(x)的单调区间需满足2kπ-π/2≤2x-π/6≤2kπ+π/2,即kπ-π/6≤x≤kπ+π/3,k∈Z