已知函数y=1/x+2/(1-x)(0

问题描述:

已知函数y=1/x+2/(1-x)(0

题目错了,没有最大值,只有最小值.
利用均值不等式
y=1/x+2/(1-x)
=[x+(1-x)]*[1/x+2/(1-x)]
=1+2x/(1-x)+(1-x)/x+2
= 3+2x/(1-x)+(1-x)/x
≥ 3+2√[2x/(1-x) *(1-x)/x]
=3+2√2
当且仅当 2x/(1-x)=(1-x)/x时等号成立
∴ 函数y=1/x+2/(1-x)(0