1)f(x)=2cos^2x+2√3sinxcosx+m
=cos2x+√3sin2x+m+1
=2sin(2x+π/6)+m+1
最小正周期T=2π/2=π
2)f(x)在[-π/6,π/6]上时2x+π/6∈[-π/6,π/2]
则f(x)∈[m,m+3]
由m+m+3=3得m=0