For the following function, a$)$ give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b$)$ identify intervals where the function is increasing or decreasing; c$)$ give the coordinates of any points of inflection; d$)$ identify intervals where the function is concave up or concave down, and e$)$ sketch the graph.

$q(x)=\frac{x}{x^2+16}$

a$)$ What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box$($es$)$ to complete your choice.

A$.$ The relative minimum point$($s$)$ is$/$are and there are no relative maximum point$($s$).$

$($Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.$)$

B$.$ The relative maximum point$($s$)$ is$/$are and there are no relative minimum point$($s$).$

$($Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.$)$

C$.$ The relative minimum point$($s$)$ is$/$are and the relative maximum point$($s$)$ is$/$are

$($Simplify your answers. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.$)$

D$.$ There are no relative minimum points and there are no relative maximum points.