1. (5 points) Find a rectangle with the greatest area among all the rectangles with the xed perimeter p. Express the maximum area of the rectangle in terms of p. 2. (5 points) Sketch the graph of a function that satises a_ll of the following conditions. Explain! o f(0) = O, and f'(2) = f'(1)= f'(9) = 0 o 33:10 f(:r:) = 0 and 331123 f(:r:) = 00 o f'(:5) 0 on (2, 1) and (6,9) 0 f\"(a:) > 0 on (oo,0) and (12,00) 0 f\"(:t)