text: # Calculus
  
  posted by .
  
  Determine the function is concave upward and where it is concave downward
  f(x)= x / (x+1)
  
  • Calculus -
  
  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 -
  
  I think you dropped a minus sign on f'', so the intervals are reversed.
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