Question

已知函数f(x)=2sin(2x+π/6)x∈R 1.求函数f(x)的最小正周期及单调增区间

Answer 1

1、函数f(x)的最小正周期T=2 π/2=π

令-(π/2)+2kπ≤2x+π/6≤π/2+2kπ,k∈Z,则-(π/3)+kπ≤x≤π/6+kπ,k∈Z

函数f(x)的单调增区间是【-(π/3)+kπ,π/6+kπ】,k∈Z

2、当x∈(π/4,3π/4]时,2π/3