Find the inflection points and where the function is concave up and concave down:
f(x)=x/(x+x^2)
I suspect a typo, since what you have written is just
f(x) = x/(x+x^2) = 1/(1+x)
f' = -1/(1+x)^2
f" = 2/(1+x)^3
Anyway, fix that, find f", and recall that
f"=0 means an inflection point
f" > 0 means concave up
f" < 0 means concave down