f(x)=4cosxsin(x+π/6)-1
=4cosx(√3/2sinx+1/2cosx)-1
=2√3sinx+2cos^2x-1
=√3sin2x+cos2x
= 2sin(2x+π/6)
x∈[-π/6,π/4],则（2x+π/6）∈[-π/6,2π/3]
画个单位圆,一比划就出来了
所以f（x）最大值为2,最小值为-1