1.a=(根号3msinx,cosx) b=(cosx,-mcosx)
f(x)=ab=√3msinxcosx-mcosxcosx
=(√3/2)msin2x-(m/2)[2(cosx)^2-1+1]
=msin2xcosπ/6-mcos2xsinπ/6-m/2
=msin(2x-π/6)-m/2
x∈[0,π/2]时,2x-π/6∈[-π/6,5π/6],sin(2x-π/6)∈[-1/2,1]
m>0,f(x)最小值=-m/2-m/2=-m=-4 m=4
最大值=m-m/2=m/2=2,2x-π/6=π/2 x=π/3
m