若-3≤log(1/2) x≤(-1/2),求f(x)=(log2 x/2)*(log2 x/4)的最大值和最小值

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若-3≤log(1/2) x≤(-1/2),求f(x)=(log2 x/2)*(log2 x/4)的最大值和最小值
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若-3≤log(1/2) x≤(-1/2),求f(x)=(log2 x/2)*(log2 x/4)的最大值和最小值
若-3≤log(1/2) x≤(-1/2),求f(x)=(log2 x/2)*(log2 x/4)的最大值和最小值

若-3≤log(1/2) x≤(-1/2),求f(x)=(log2 x/2)*(log2 x/4)的最大值和最小值
-3≤log(1/2) x≤(-1/2),
1/2≤log2(x)≤3
f(x)=[log2(x)-log2(2)][log2(x)-log2(4)]
令a=log2(x)
y=(a-1)(a-2)=(a-3/2)²-1/4
1/2≤a≤3
所以a=3/2,f(x)最小=-1/4
a=3,f(x0最大=2

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