Question

已知函数f（x）=（log2 x/8)(log2 x/4)(2《x《8）求其最大值，最小值。

已知函数f（x）=（log2 x/8)(log2 x/4)(2《x《8）求其最大值，最小值。
要过程!!

Answer 1

f(x)=[log2(x)-log2(8)][log2(x)-log2(4)]
=[log2(x)-3][log2(x)-2]
令a=log2(x)
2<=x<=8
log2(2)<=log2(x)<=log2(8)
所以1<=a<=3

y=f(x)=(a-3)(a-2)
=a²-5a+6
=(a-5/2)²-1/4
1<=a<=3
所以a=5/2,y最小=-1/4
a=1，y最大=2

所以f(x)最大值=2，最小值=-1/4

Answer 2

f(x)=(log2 x -3)(log2 x - 2)
=(t-3)(t-2) (设t=log2 x，则1《t《3)
当t=5/2最小，f=-1/4
当t=1最大，f=2

Answer 3

f(x)=log2(x/8)*log2(x/4)
=[log2(x)/log2(8)]*log2(x)/log2(4)
=[log2(x)/3]*[log2(x)/2]
=x/6
因为2《X《8如果是x大于等于2小于等于8就自己去求吧