总题干：已知函数f(x)=2sin(2x+π/6)

1) f(x)=2sin(2x+π/6)
∵ sin(2x+π/6)≤1,且2x+π/6=2kπ+π/2(其中k是整数）时sin(2x+π/6)=1
∴X=Kπ+π/6时（其中k是整数）,f(x)最大值f(x)=2
2) 2x+π/6=kπ（其中k是整数）时,sin(2x+π/6）=0
∴x=kπ-π/12(其中k是整数）时,f(x)=0