f(x)=根号3+4根号3cos^2x-2sin2x=根号3+2根号3cos2x-2sin2x+2根号3=3根号3+2根号3cos2x-2sin2x=3根号3+4[cos2xsin(π/3)-cos(π/3)sin2x]=3根号3+4cos(2x+π/3)
最小值为3根号3-4 π/4≤x≤7π/24 π/2