xy5878
幼苗
共回答了11个问题采纳率:100% 举报
由f(x)=[log2(x/4)][log2(x/2)]
=[log2(x)-log2(4)][log2(x)-log2(2)]
=[log2(x)-2][log2(x)-1]
=log²2(x)-3log2(x)+2
=[log2(x)-3/2)²-9/4+2
=[log2(x)-3/2]²-1/4
∵x∈[√2,8],且底a=2>0,
∴f(x)在[√2,8]上是增函数,
(1)当x=3/2时,f(x)最小值ymin=-1/4.
(2)当x=8时,f(x)的最大值ymax=[log2(8)-3/2]²-1/4
=(3-3/2)²-1/4
=2.
1年前
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