** **

EGET 3171

** **

**Chapter 3: Applications of the Derivative**

1. A metal cylindrical container is to hold 64 cubic inches. Find the dimensions which use the minimum amount of material of metal for:

a) an open container (r = 2.73 inches)

b) a closed container (r = 2.17 inches)

2. An airplane leaves a field at noon and flies east at 100 km/h. A second airplane leaves the same field at 1pm and flies south at 150 km/h. How fast are the airplanes separating at 2pm? (170 km/h)

3. A person 5 feet tall walks at the rate of 4 ft/sec directly away from a street light which is 20 feet above the street. At what rate is the length of her shadow changing? (1.33ft/sec)

4. Determine the dimensions of a cylinder with maximum lateral surface area which can be inscribed inside a sphere of radius 8 inches. (r = 5.66 inches)

5. A solution is passing through a conical filter 24 inches deep and 16 inches across the top into a cylindrical vessel with diameter 12 inches. At what rate is the level of the solution in the cylinder rising when the depth of the solution in the filter is 12 inches and its level is falling at 1 inch/min? (0.444in/min)