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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