$(1$ point$)$

Consider $f(x)=\frac{x}{x^2+1}.$

Note : Use round parentheses for your intervals $($open interval notation$).$ Separate multiple intervals with commas. For example, if the function is increasing between $-2$ and $0,$ and then again between $3$ and infinity, you should write your answer as $,$ infinity$).$

The inflection points for $f(x)$ are $($Note : List the coordinate points, with an $x$ and $y$ values. Separate multiple points with commas$)$:

The function is concave up in the region

The function is concave down in the region