Let $\displaystyle f(x) = \frac{1}{3x^{2}+6}$. Find the open intervals on which $f$ is concave up (down). Then determine the $x$-coordinates of all inflection points of $f$.

 1 $f$ is concave up on the intervals 2 $f$ is concave down on the intervals 3 The inflection points occur at $x$ =

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

In the last one, your answer should be a comma separated list of $x$ values or the word "none".

Your overall score for this problem is