问题 解答题
已知x满足:2(log
1
2
x)2+7log
1
2
x+3≤0
,求f(x)=(log2
x
2
)•(log2
x
4
)
的最大值和最小值.
答案

2(log

1
2
x)2+7log
1
2
x+3≤0,∴
1
2
≤log2x≤3

∵求f(x)=(log2

x
2
)•(log2
x
4
)=(log2x-1)(log2x-2)=(log2x)2-3log2x+2,

f(x)=(log2x-

3
2
)2-
1
4

f(x)max=f(x)

.
log2x=3
=2,f(x)min=f(x)
.
log2x=
3
2
=-
1
4

故求f(x)=(log2

x
2
)•(log2
x
4
)的最大值是2,最小值是-
1
4

单项选择题 A1/A2型题
单项选择题