f(x)=2√3sinxcosx +2cos²x-1 =√3sin2x+ 1+ cos2x-1 ==√3sin2x+cos2x =2sin(2x+π/6) 最小正周期=πx【0,π/2】 2x+π/6【π/6,7π/6】最大值为2 最小值为02kπ+π/2<2x+π/6<2kπ+3π/2kπ+π/6