银杏树美食和药用:f(x)=xlog2(x)+(1-x)log2(1-x) (0<x<1) 求f(x)最小值

来源：百度文库 编辑：高考问答 时间：2024/05/11 04:07:37
f(x)=xlog2(x)+(1-x)log2(1-x)
不是f(x)=2log2(x)+2log2(1-x)
请写下简要步骤

=log2(x^2)+log2[(1-x)^2]
=log2[x^2*(1-x)^2]
=log2[(x^2-x)^2]
x=1/2时x^2-x取得最小值-1/2
f(x)最小值=log2(1/4)
=-2

-1

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