You are given the function $f(x)=\frac{1}{x^2+3}$.
$f(x)$ is concave up whenever:

A. $3x^2-3$ is positive.
B. $3x^2+3$ is negative.
C. $x^2-3$ is negative.
D. $3x^2-3$ is negative.
E. $x^2+3$ is negative.
F. $3x^2+3$ is positive.

$f(x)$ is concave down whenever:

A. $3x^2+3$ is positive.
B. $3x^2-3$ is positive.
C. $3x^2+3$ is negative.
D. $x^2+3$ is negative.
E. $3x^2-3$ is negative.
F. $x^2-3$ is negative.

The points of inflection of $f(x)$ are the same as:

A. the zeros of $x^2-3$.
B. the zeros of $3x^2-3$.
C. the zeros $x^2+3$.
D. the zeros of $3x^2+3$.