f(x)=log2(x/4)×log2(x/2)
=[log2(x)-log2(4)]×[log2(x)-log2(2)]
=[log2(x)-2]×[log2(x)-1]
令t=log2(x)
∵x∈[2,8]
∴t=log2(x)∈[1,3]
f(x)=(t-2)(t-1)=t²-3t+2=(t-3/2)²-1/4
∵t=3/2在区间[1,3]内
∴fmin=f(t=3/2)=-1/4
fmax=f(t=3)=2