13) Analyze and sketch each function using the algorithm for curve sketching a) Mac) = ix" 3x2 14) Consider the graph to the right. 14 7 y a) How many times does the function have a 13 Position (meters) derivative = 0? How do you know? 12 - 11- 10 - 9 - b) State the sign of the first and second derivatives at the following times. i) t = 3 s ii) t = 7 s iii) t = 10 s -2 10 11 12 13 14 Time (seconds) 15) A garbage can is in the shape of a cylinder with no lid. It needs to have a volume of 5000 cm3. What will be the radius and height of the can that uses the least amount of material to construct it? (Hint: Surface Area)16) A carpenter builds an open box with a square base. She has 8 m2 of wood available. Find the volume of the largest box she can build. 17) Sandy will make a closed rectangular jewellery box with a square base from two different woods. The wood from the top and botton costs $0.0020/cm3. The wood for the sides costs $0.0030/cm2. Find the dimensions that minimize the cost for a box with volume 4000 cm3. 18) A music store sells an average of 120 CDs per week at $24 each. A market survey indicates that for each $0.75 decrease in price, five additional CD5 will be sold per week. The cost of producing x CD5 is 60:) = 0.003x2 + 3x + 2000. What price and quantity of CD5 maximizes profit