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Thoroughly investigate the graph of . Identify all important qualities, such as where the function is increasing, decreasing, concave up, and concave down. Also identify point(s) of inflection, extrema, intercepts, and provide graphs of and . Be sure to justify all statements both graphically and analytically.

Solve to locate the extrema and determine the increasing/decreasing intervals.
Solve to determine points of inflection and the intervals of concavity.