Calculus
posted by Cam .
Determine the function is concave upward and where it is concave downward
f(x)= x / (x+1)

f ' (x) = ( x+1  x)/(x+1)^2 = (x+1)^2
f ''(x) = 2(x+1)3
= 1/(x+1)^3
if x > 1 , f ''(x) is positive, so the curve is convace upwards
if x < 1, f ''(x) is negative, so the curve is concave downwards.
notice x ≠ 1, so there is a vertical asymptote at x + 1 = 0 
I think you dropped a minus sign on f'', so the intervals are reversed.