f(x)=sin(x-π/6)cosx
=（sinxcosπ/6-cosxsinπ/6)cosx
=√3/2*sinxcosx-1/2*cos²x
=√3/4sin2x-1/4*(1-cos2x)
=√3/4sin2x+1/4*cos2x)-1/4
=1/2sin(2x+π/6)-1/4
∵ x属于（0,派/2）
∴ 2x+π/6∈[π/6,7π/6]
∴ -1/2≤sin(2x+π/6)≤1
∴ f(x)的值域为[-1/4,1/4]
2
f'(x)=1/2*cos(2x+π/6)*2=cos(2x+π/6)
曲线y=f(x)在x0处的切线
倾斜角a属于[arctan1/2,派/4]
∴斜率k∈[1/2,√2/2]
∴1/2≤cos(2x0+π/6)≤√2/2
∵ 2x0+π/6∈[π/6,7π/6]
∴ π/4≤2x0+π/6≤π/3
∴π/24≤x0≤π/12