$$f(x) = \dfrac{2}{x^2 + 1}$$

a) Find the first and second derivatives.
$f'(x) =$
$f''(x) =$

b) Identify the graph that displays $f$ in blue and $f''$ in red. ? A B C D

A.     B.


C.     D.

c) Using the graphs of $f$ and $f''$, indicate where $f$ is concave up and concave down. Give your answer in the form of an interval.

NOTE: When using interval notation in WeBWorK, remember that:
        You use 'INF' for $\infty$ and '-INF' for $-\infty$.
        And use 'U' for the union symbol.
Enter DNE if an answer does not exist.

$f$ is concave up on

$f$ is concave down on