f(x)＝√3sinxcosx－cos²x＝√3/2sin(2x)－1/2cos(2x)－1/2＝sin(2x－π/6)－1/2
(1)最小正周期T＝2π/2＝π
(2)x∈[0,π/2] ∴2x∈[0,π] ∴2x－π/6∈[﹣π/6,5π/6]
∴sin(2x－π/6)∈[﹣1/2,1] ∴f(x)∈[﹣1,1/2]
∴函数f(x)的最大值为1/2,最小值为﹣1