Question

f(x) = (x-4)/ (x^2)

I need to use interval notation to indicate where f(x) is concave up or down.

Concave up is (12, inf) but I can't figure out concave down. Help!

Answer 1

I will assume that you had y'' = 2(x-12)/x^4

f(x) will be concave up when y" > 0
and concave down when y" < 0

we don't have to worry about x^4, it will always be positive, except when x = 0 , which is a restriction on f(x) anyway.

I don't see why you correctly got x > 12 for concave up, and could not see
x < 12 for concave down ?