A rectangle in the first quadrant is inscribed with its base on the x-axis and its upper corners on the parabola y = 3600 - x^2 -. What are the dimensions of such a rectangle with the greatest possible area? [A] First, find the area as a function of x: A(x) = [B] Find the domain of A in the context of the problem. Domain: [C] Find A' (x) А' (x) = [D] Find the critical value(s) within the appropriate domain of A. No decimal entries allowed. [E] Determine where A is increasing and where A is decreasing on its appropriate domain. Increasing: Decreasing: [F] What is the best conclusion with regards to an absolute extrema at the critical value. • Since the A goes from increasing to decreasing, by the first derivative test we have an absolute maximum at the critical value O The results are inclusive, another test besides the first derivative needs to be performed in order to determine if there is an absolute maximum or minimum at the critical value • Since the A goes from decreasing to decreasing, by the first derivative test we have an absolute maximum at the critical value • Since the A goes from decreasing to increasing, by the first derivative test we have an absolute minimum at the critical value • Since the A goes from increasing to decreasing, by the first derivative test we have an absolute minimum at the critical value [G] What is the maximize area of the rectangle. No decimal entries allowed. Maximum Area =