[16 marks] Consider the function f (x) = - (a) State the domain of f using interval notation. (b) By hand, determine any r-intercepts and y-intercepts of f. (c) By hand, find all horizontal asymptotes of f (if any). Justify your answer. (d) By hand, determine any vertical asymptotes of f. (e) Given that f'(x) = T- - 18 T4 , determine the interval(s) on which f is increasing and on which f is decreasing. State any relative maximum/minimum values. (f) Given that f"(x) = _2(X- - 36) , determine the intervals of concavity for f. Show all work and leave results as exact values. (g) By hand, sketch f using the information found in parts (a)-(f). Be sure to label the graph with all intercepts, asymptotes, relative maxima and minima, and inflection points