1. (5 points) Find a rectangle with the greatest area among all the rectangles with the fixe perimeter p. Express the maximum area of the rectangle in terms of p. 2. (5 points) Sketch the graph of a function that satisfies all of the following conditions. Explain . f(0) = 0, and f'(-2) = f'(1) = f'(9) = 0 . lim f(x) = 0 and lim f(x) = -00 I-+00 . f'(x) 0 on (-2, 1) and (6, 9) . f"(a) > 0 on (-oo, 0) and (12, 00) . f"(a)