函数y=2lg(x+2)-lg(x+1) (x>-1)的最小值是?

问题描述:

函数y=2lg(x+2)-lg(x+1) (x>-1)的最小值是?

y=2lg(x+2)/(x+1)

y=lg(x+2)^2/(x+1)
(x+2)^2/(x+1)
=x+3+1/(x+1)
=(x+1)+1/(x+1)+2
>=2*根号[(x+1)*1/(x+1)]+2=2+2=4,
当(x+1)=1/(x+1),即x=0时,取等号.
当 x=0时,
y=2lg(x+2)-lg(x+1) (x>-1)有最小值=lg4