如何算x^2+x+1/(x+1)这类函数的最值?

Question

如何算x^2+x+1/(x+1)这类函数的最值?

Answer 1

f(x)=(x^2+x+1)/(x+1)
=(x+1)^2-(x+1)+1/(x+1)
=x+1-1+1/x+1
令x+1=t
f(t)=t+1/t-1(t≠0)
t>0
f(t)≥2√t*1/t-1=1
t0
f(t)=-(-t+(1/(-t)))-1≤-2-1=-3
(-R,-3]U[1,R)