f(x)=2sin²x＋2sinxcosx=1－cos2x＋sin2x=√2sin(2x－π/4)＋1.T=2π/2=π,最小1－√2,对称2x－π/4=kπ＋π/2,即x=kπ/2＋3π/8,对称中心2x－π/4=kπ,即(kπ/2＋π/8,1),增区间[kπ－π/8,kπ＋3π/8]