CK-12-Calculus

http://www.ck12.org Chapter 3. Applications of Derivatives

HencedVdt =^1275 πh^2 dhdt, and by substitution,

5 =^1275 π( 36 )dhdt

dh

dt=

375

432 π≈^0.^28

ft

min.

Lesson Summary

1. We learned to solve problems that involved related rates.

Multimedia Links

For a video presentation of related rates(12.0), see Math Video Tutorials by James Sousa, Related Rates (10:34).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/546

In the following applet you can explore a problem about a melting snowball where the radius is decreasing at a
constant rate. Calculus Applets Snowball Problem. Experiment with changing the time to see how the volume
does notchange at a constant rate in this problem. If you’d like to see a video of another example of a related rate
problem worked out(12.0), see Khan Academy Rates of Change (Part 2) (5:37).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/547

Review Questions

1..
a. Make up a related rates problem about the area of a rectangle.
b. Illustrate the solution to your problem.
2. Suppose that a particle is moving along the curve 4x^2 + 16 y^2 = 32 .When it reaches the point( 2 , 1 ),the
x−coordinate is increasing at a rate of 3 ft/sec. At what rate is they−coordinate changing at that instant?