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1. Consider the fimction f(:r) 12) Note that 8x(x2 + 12) and f" (r) and the .T-intercept of the graph of f is approximately 1.3146. (a) Evaluate all the necessary limits to identify all the linear asymptotes of the graph (2 points) of f (b) Construct a table of signs for f' and f" that specifies the following: (4 points) i. the intervals on which the graph of f is increasing, decreasing, concave up, and concave down, and ii. the values of m; at which f has relative extrema, inflection points, and vertical asymptotes (if any). (c) Sketch thc graph of f with emphasis on concavity. Label all thc intercept points, relative extremum points, inflection points, and holes (if any) with their coordinates. Show the asymptotes of the graph of f and label them with their respective equa- (4 points) tions.