AGENDA: 1. Copy Notes on Related Rates and work all examples

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Presentation transcript:

OBJECTIVE: Modeling Rate of Change – Interpret the derivative as a rate of change. AGENDA: 1. Copy Notes on Related Rates and work all examples 2. Watch videos on Related Rates 3. Assignment: p. 245 {4,6,8,9,10,11,12,19,23,24} 4. Hand out review for FINAL

Related rates Section 3.9

Related Rates A problem that has an equation relating two or more things which change over time, and we want to find the derivative of one of the functions at a particular time.

Related Rates List of known rates List of wanted rates Equation relating the variables in the known and wanted rates Differentiate implicitly Solve for the wanted rate Substitute the known and calculated values

Example #1 A point moves along the curve In such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when ?

Example #2 A spherical balloon is inflated at the rate of 20 cubic feet per minute. How fast is the radius increasing when r= 2ft?

Example # 3 A conical tank (vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change of the depth of the water the instant it is 8 feet deep.

Example #4 25 y x A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. A. How fast is the top moving down the wall when the base of the ladder is 7 feet from the wall?

B. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall. 25 x

Helpful Videos on Related Rates Filling up a balloon – 5 minutes http://www.youtube.com/watch?v=WlBpPpE-XRg How fast is the ladder moving? – 7 minutes http://www.youtube.com/watch?v=8M11k0WPcMc How fast does the camera need to move to keep up with the plane? – 10 minutes http://www.youtube.com/watch?v=h2IqQmvIYWo KHAN ACADEMY Pouring water into a cone – 11 minutes http://www.youtube.com/watch?v=Xe6YlrCgkIo How fast is the ladder moving down? – 6 minutes http://www.youtube.com/watch?v=kBVDSu7v8os How fast is the balloon rising? http://www.youtube.com/watch?v=_kbd6troMgA