1) All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the total surface area of the cube changing when each edge is 10 cm? 2): The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing? 3): A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. The winch pulls in rope at a rate of 4 ft/s. Determine the speed of the boat when there is 13 feet of rope out. Optional Challenge worth 3 bonus points: What happens to the speed of the boat as it gets closer to the dock (all work must be shown to receive extra points) Part B (optimization problems) 4): Find 2 numbers whose sum is 60 and whose product is a maximum. 6 points 5): A poster is to have an area of 180 in? with 1-inch margins at the bottoms and sides, and a 2-inch margin at the top. What dimensions (of the poster) will give the largest printing area? 10 points 6): A right circular cylinder is inscribed in a sphere of radius "". Find the largest possible volume of such a cylinder in terms