James watches 3 times as many movies a month as half of the square of the amount of movies Lina watches a month, and Sarah watches 5 fewer movies than James. Model the product of the amount of movies they watch per month with respect to the amount of movies Lina watches. a. Analyze the function represented by the problem using the first and second derivatives to find local extrema points and points of inflection. b. Do interval tests with each derivative to find intervals of increase and decrease and intervals of concavity. c. d. If the function is rational, find any asymptotes. Sketch a graph of the function, the first derivative, and the second derivative on large paper (use different colors for each function)