Yet another (fictional) student submitted the following solution to an optimization problem. This time the solution is technically correct, but it is still insufficient: there isn't nearly enough detail/explanation to receive full credit. Rewrite the solution below, adding all details (including a diagram) that are necessary to produce a complete solution worthy of full marks. To be clear: the final answer is correct. What we want to see are the necessary explanations to make it clear where each step is coming from.) Problem: Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the cy-plane as the top half of the circle x2 + y? = 9.) Solution: A = 2xy = 2x\\/9-x2 A' = 29-x2 2(9 - 2x2) V9 - x2 V9 - x2 2x = 9 sox = - Dimensions: 2x = 3v2 and y =