(4 pts.) Find the maximum area of a rectangle inscribed between the x-axis and the function f(x) = x4 +3. (4 pts.) Find two numbers whose sum is 23 and whose product is a maximum. (5 pts.) Suppose we want to enclose a field in the shape of a rectangle with a semicircle on one end: If we have 500 feet of fencing, what is the maximum area we can enclose? (4 pts.) A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions that minimize the cost of the metal to make the can. For the next problem, explain and justify your answers. (3 pts.) The derivative function f'(JC) is shown below (continued on the next page)