Consider the polynomial function g(x)=x3−6x2+9x+4 defined for all real x.
(a) Compute g′′(x).
(b) Solve g′′(x)=0 to obtain all potential x–values at which the concavity of the graph of g might change.
(c) Determine the intervals of concavity of g on the real line. Show the analysis that leads to your conclusions.
(d) For every x–value found in part (b), decide whether the point lies on the graph of g and whether it is an inflection point. State the coordinates of each actual inflection point, if any, and justify your answer.