(1)當2x－π/3＝2kπ＋π/2即x＝kπ＋5π/12時,f(x)取得最大值1
當2x－π/3＝2kπ－π/2即x＝kπ－π/12時,f(x)取得最小值﹣3
(2)∵x∈[﹣π/2,π/2] ∴2x－π/3∈[﹣4π/3,2π/3]
∴當2x－π/3∈[﹣π/2,π/2]即x∈[﹣π/12,5π/12]時,函數(shù)單調(diào)遞增
∴當x∈[﹣π/2,π/2]時函數(shù)的增區(qū)間為：[﹣π/12,5π/12]
(3)∵f(x)＝2sin(2x－π/3)－1＝2sin[2(x－π/6)]－1
∴函數(shù)的圖象可以由函數(shù)y=sin2x的圖像先沿x軸方向向右偏移π/6個單位,再沿y軸方向向下平移1個單位