In the graph below, a rectangle is inscribed with its base on the x-axis and its upper corners on the ellipse x + , = 1. (a) Find the dimensions of such a rectangle with the greatest possible area. (b) Show that the dimensions you found produce a local maximum for the area using the first or the second derivative test. You do not need to argue that your answer is a global maximum. (c) What is the resulting maximum area? Enter the maximum area in the blank below. Round your answer to two decimal places. 35 3 2.5 21 1.5 (x;y) 1 0.5# X -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8