f(x)=2sin(-2x+π/3)
1.
最小正周期T=2π/2=π
2.
f(x)=-2sin(2x-π/3)
f(x)的递减区间即是sin(2x-π/3)的递增区间
由2kπ-π/2≤2x-π/3≤2kπ+π/2,k∈Z
得kπ-π/12≤x≤kπ+5π/12,k∈Z
∴f(x)递减区间为[kπ-π/12,kπ+5π/12],k∈Z
3
由2x-π/3=kπ+π/2,k∈Z
得对称轴x=kπ/2+5π/12,k∈Z
由2x-π/3=kπ,k∈Z
得x=kπ/2+π/6,k∈Z
对称中心为(kπ/2+π/6,0)k∈Z