f(x)=sin(2ωx-π/6)-4sin²ωx+2
=√3/2sin2ωx-1/2cos2ωx-4sin²ωx+2
=√3/2sin2ωx-1/2cos2ωx+2(cos2ωx-1)+2
=√3/2sin2ωx+(3/2)cos2ωx
=√3sin(2ωx+φ),tanφ=√3→φ=π/3
∵相邻两个交点的距离为π/2,最小正周期=π
∴2π/2ω=π→ω=1
解析式：f(x)=√3sin(2x+π/3)
(2)g(x)=√3sin(2x+π/3+m) 三角函数在平移的时候是左加右减
将(-π/3,0)代入:
0=√3sin(-2π/3+π/3+m)
m=2kπ+π/3 最小值，m=π/3
∴g(x)=√3sin(2x+2π/3)
g'(x)=2√3cos(2x+2π/3)
驻点：2x+2π/3=2kπ±π/2
即x=kπ-π/12、x=kπ-7π/12
在[-π/6,7π/12]上的单调递增区间为x∈[-π/6,-π/12) (g'(x)>0)