已知x满足不等式2(log1/2x)^2+9og1/2x+9≤0.求函数f(x)=(log2x/4)(log2x/2)的最大值和最小值

2(log1/2x)^2+9og1/2x+9≤0
(2log1/2x+3)(log1/2x+3)≤0
-3≤log1/2x≤-3/2
(1/2)^(-3)≥x≥(1/2)^(-3/2)
8≥x≥2√2

f(x)=(log2x/4)(log2x/2)
=(log2(x)-log2(4))*(log2(x)-log2(2))
=(log2(x)-2)*(log2(x)-1)
=(log2(x))^2-3log2(x）+2
=[log2(x)-3/2]^2+2-9/4
=[log2(x)-3/2]^2-1/4

当x=2√2=2^(3/2)时，函数最小值为-1/4
当x=8时，函数最大值为
[log2(8)-3/2]^2-1/4
=（3-3/2）^2-1/4
=2