Consider the rational function g(x)=x2−9x+2, whose domain is all real numbers except x=±3.
(a) Compute g′(x) and simplify completely.
(b) Determine all x–values in the domain of g at which g′(x)=0. State each value exactly.
(c) Using the values from part (b) together with the vertical asymptotes, indicate every open interval contained in the domain of g and decide on which of those intervals g is increasing or decreasing. Show algebraic reasoning to support each conclusion.
(d) Identify the x–coordinate of every relative extremum of g that lies in its domain, and state whether each is a relative maximum or a relative minimum. Justify fully.