f(x)=√3(cos2x+1)-sin2x-√3
=√3con2x-sin2x
=2cos(2x+π/3)
∴(1) 函数最小正周期:T=π
当2x+π/3=2kπ-π/2时,函数取最小值,集合为{x=kπ-5π/12}
(2) 当2kπ-π/2≤2x+π/3≤2kπ+π/2时,函数递增,增区间为(kπ-5π/12,kπ+π/12)
(3) f(π/3)=-2
又∵f'(x)=-4sin(2x+π/3)
∴ f'(π/3)=0
∴ 切线方程为 y=-2