Question

What are the points of inflection of #f(x)=2 / (x^2 - 9) #?

Answer 1

There are no points of inflection for the graph of this function.

Explanation:

`f(x) = 2/(x^2-9)` has domain all reals except `3`, `-3`.

`f''(x) = (12(x^3+3))/(x^2-9)^3`

`f''` changes sign, so concavity changes, at `x=-3` and at `x=3`.

A point of inflection is a point on the graph at which the concavoty changes.

The graph of this function does not have points with `x=3` or `x=-3`. So it has no inflection points.