求y=(x^2+3x+5)/(x+1) (x>-1)最小值
问题描述：
求y=(x^2+3x+5)/(x+1) (x>-1)最小值
答
y=(x^2+3x+2+3)/(x+1)
=(x+1)(x+2)/(x+1)+3/(x+1)
=x+2+3/(x+1)
=(x+1)+3/(x+1)+1
x>-1
x+1>0
所以y>=2√(x+1)*3/(x+1)+1=2√3+1
当x+1=1/(x+1)时取等号
x+1=1,x=0>-1
所以等号能取到
所以y最小值=2√3+1