1. 4.1: Related Rates Greg Kelly, Hanford High School, Richland, Washington

2. First, a review problem: Consider a sphere of radius 10cm. If the radius changes 0.1cm (a very small amount) how much does the volume change? The volume would change by approximately. At 10cm At 10.1cm This is an example of a secant line problem!!

3. Now, suppose that the radius is changing at an instantaneous rate of 0.1 cm/sec. (Possible if the sphere is a soap bubble or a balloon.) The sphere is growing at a rate of. Note: This is an exact answer, not an approximation like we got with the differential problems.

4. Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping? Find ( r is a constant.) (We need a formula to relate V and h. )

5. Steps for Related Rates Problems: 1. Draw a picture (sketch). 2. Write down known information. 3. Write down what you are looking for. 4. Write an equation to relate the variables. 5. Differentiate both sides with respect to t. 6. Evaluate.

6. Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

7. Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

8. B A Truck Problem: Truck A starts 4 miles east of Chicago and travels west (towards Chicago) at 40 mi/hr. Truck B starts 3 miles north of Chicago and travels north (away from Chicago) at 30 mi/hr. How fast is the distance between the trucks changing at that instant?

9. B A Truck Problem: How fast is the distance between the trucks changing? Truck A travels west at 40 mi/hr. Truck B travels north at 30 mi/hr. 