f(x)=√3sinxcosx-cos²x-1/2
=√3/2(2sinxcosx)-1/2(1+cos2x)-1/2
=√3/2sin2x-1/2cos2x-1
=sin2xcosπ/6-cos2xsinπ/6-1
=sin(2x-π/6)-1
故 f(x)的最小正周期是 π,最小值是 -2.