y=g(x)=2log2(x+2)
x属于(-2,正无穷)
F(x)=f(x)-g(x)=log2(x+1)-2log2(x+2)
=log2(x+1)-log2(x+2)^2
=log2[(x+1)/(x+2)^2]
求F(x)最大值就是求[(x+1)/(x+2)^2]最大值求
(x+2)^2/(x+1)最小值
(x+2)^2/(x+1)
=(x+1)+1/(x+1)+2
(x+1)+1/(x+1)>=2根号下1
当x=0时等号成立
(x+2)^2/(x+1)最小值是4
[(x+1)/(x+2)^2]最大值是1/4
F(x)=f(x)-g(x)的最大值为-2