Posted by Cam on Wednesday, March 20, 2013 at 8:59pm.
Determine the function is concave upward and where it is concave downward
f(x)= x / (x+1)

Calculus  Reiny, Wednesday, March 20, 2013 at 10:24pm
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

Calculus oops  Steve, Thursday, March 21, 2013 at 4:39am
I think you dropped a minus sign on f'', so the intervals are reversed.
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