已知x满足不等式2(log2x)^2-7log2x+3小于等于0求函数F(X)=LOG2(X/2)*LOG2(X/4)的最大值和最小值
问题描述:
已知x满足不等式2(log2x)^2-7log2x+3小于等于0
求函数F(X)=LOG2(X/2)*LOG2(X/4)的最大值和最小值
答
2(log2x)^2-7log2x+31/2=
=(log2 x -1)(log2 x -2)
=(log2 x)^2-3log2 x +2
=(log2 x -3/2)^2-1/4
所以F(x)最小值在对称轴log2 x=3/2处取得,最小值为-1/4;
F(x)最大值在log2 x=3处取得,为2