已知x>1,求函数y=(x2-3x+4)/(x-1)的最小值

问题描述:

已知x>1,求函数y=(x2-3x+4)/(x-1)的最小值

y=(x2-3x+4)/(x-1)
=(x2-2x+1-x+1+2)/(x-1)
=x-1-1+2/(x-1)
=(x-1)+2/(x-1)-1
由均值不等式得到x=1+根号2时函数值最小为2根号2-1