最大值是3,则A=3.
函数周期是π,则2π/w=π,w=2.
f(x)=3sin(2x+α)
当x=π/6时f(x)取得最大值3,
则3=3sin(π/3+α),π/3+α=π/2,α=π/6.
∴f(x)=3sin(2x+π/6).
由已知得：y=g(x)= 3sin(2(x-m)+π/6)= 3sin(2x-2m+π/6).
若y=g(x)是偶函数,则g(x)=±cosx.
所以-2m+π/6=kπ+π/2,k∈Z.
m=- kπ/2-π/6, k∈Z.
∵m>0, ∴k=-1时,m的最小值是π/3.