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 Problems
1. 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. B
Phoebe 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?