2.6 Related Rates

When ice cream melts and drips out of the bottom of the cone, the volume, radius, and height of the ice cream level are all functions of time.

What function relates these three variables?

Solving Related Rate Problems1. Draw a picture and name variables

and constants

2. Write down numerical information (in terms of the variables you have chosen.)

3. Write down what you are asked to find.

4. Write an equation that relates the variables.

5. Differentiate with respect to t.

6. Evaluate.

Ex. A: Ripples in a Pond

A pebble is dropped into a calm pond. The radius of the outer ring is increasing at a constant rate of 1 foot per second. When the radius of the outer ring is 4 feet, at what rate is the total area of the disturbed water changing?

Ex. BPhoebe is going east on Alamo Street at 40 ft/sec. Meanwhile, Calvin is going south on Heights Street at 30 ft/sec. When Phoebe is 200 feet from the intersection, Calvin is 600 feet from the intersection. At this time, is the straight-line distance between them increasing or decreasing?