Let q be the function q(x)=xln(x2+1) defined for all real numbers x.
(a) Compute q′(x) and write your answer in its simplest exact form.
(b) Find every critical number of q and list them explicitly.
(c) Determine the intervals on which q is increasing and the intervals on which q is decreasing. Support your conclusions with complete analytical evidence.
(d) Identify and classify all relative extrema of q, stating each point’s x–coordinate and whether it is a relative maximum or relative minimum. Provide full justification based on your analysis in part (c).