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

Jan 4, 2016

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

#### Explanation:

$f \left(x\right) = \frac{2}{{x}^{2} - 9}$ has domain all reals except $3$, $- 3$.

$f ' ' \left(x\right) = \frac{12 \left({x}^{3} + 3\right)}{{x}^{2} - 9} ^ 3$

$f ' '$ 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.