函数x=2根号3sinxcosx+2cos平方x-1  x属于r    函数x的单调递减  区间

问题描述:

函数x=2根号3sinxcosx+2cos平方x-1  x属于r    函数x的单调递减  区间

f(x) = 2√3sinxcosx + 2cos^2x-1
= √3sin2x + cos2x
= 2(sin2xcosπ/6+cos2xsinπ/6)
= 2sin(2x+π/6)
2x+π/6 ∈(2kπ+π/2,2kπ+3π/2)时,单调减
∴单调递减区间(kπ+π/6,kπ+2π/3)