ConcavityCalculus
posted by Lisa on .
Determine the concavity for f(x)= 4/x^21
I took the second derivative and solved for zeros. I got x=1 and x=1. However when plugged into the orig. equation this results in 4/0 (undefined). Does this mean there is no concavity?

if f = 4/(x^21)
f'' = 8(3x^2+1)/(x^21)^3
f'' is never zero.
f'' is discontinuous at x=1 and 1, and changes sign there
so, f ix concave down for x<1 and concave up for x>1