log2(x/2)*log√2(√x/2)的最大值最小值
问题描述：
log2(x/2)*log√2(√x/2)的最大值最小值
√2
答
因为√2≤x≤8
故：1/2≤log√2 √x≤3,令t= log√2√ x
故：1/2≤t≤3,
又：f（x）=log2（x/2)*log√2（√x/2)
=( log2 x- log2 2)( log√2 √ x- log√2 2)
=( log2 x- 1)( log√2 √ x- 2)
=(t-1)(t-2)
=t²-3t+2
=(t-3/2)²-1/4
故：t=3/2时,取最小值为-1/4,此时log√2 √ x=3/2,x=2√2
当t=3时,取最大值2,此时log√2 √ x=3,x=8 .