Question

F(x) = 1/(x^2-4), such that F''(x) = (6x^2-8)/(x^2-4)^3
I am asked to find the intervals of concavity and possible points of inflection. But...

Answer 1

When i set F''(x)=0 then i get a value (+-2/sqrt(3)) and WOLF says that this graph has no points of inflection (because it is asymptotic). What am i misunderstanding?

Answer 2

it is asymptotic as x -> +/- infinity. but there are discontinuities at +/-2

Answer 3

is a discontinuity considered a point of inflection?

Answer 4

the discontinuities can still bound a region of concavity