Consider the function

$f(x)=\frac{2x}{x^2-1}$

Find the domain.

Find the $x-$ and $y-$intercepts.

State the symmetry $(if$ any$).$

Find the asymptotes $(if$ any$).$

Find the intervals $of$ increase and decrease.

Find the local maxima and minima.

$Itis$ a fact that $f^{\text{'}\text{'}}(x)$ simplifies $to\frac{4x(x^2+3)}{(x^2-1{)}^3}.$ Where $is$ the graph $off$ concave $up?$ Where $isit$ concave

down?

Find the inflection points $(if$ any$).$

Using this information, sketch a graph $of$ this function $on$ a separate piece $of$ paper.