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lecture22

# lecture22 - If one travels north at 15 miles per hour and...

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Math 006 (Lecture 22) Related Rates Example 1. A 26-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 2 feet per second, at which rate is the bottom of the ladder moving away from the wall when the bottom of the ladder is 10 feet from the wall? Procedure 1. Sketch a figure. 2. Identify all relevant variables, including those rates are given and those rates are to be found . 3. Express all given rates and rates to be found as derivatives . 4. Find an equation connecting the variables identified in step (2). 5. Implicitly differentiate the equation in step (4). 6. Solve for the derivative that will give the unknown rate. 1

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Example 2. Suppose that two motorboats leave from the same point at the same time.
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Unformatted text preview: If one travels north at 15 miles per hour and the other travels east at 20 miles per hour, what is the rate of change of the distance between them after 2 hours? Example 3. Suppose that for a company manufacturing transistor radios, the cost, rev-enue, and the proļ¬t equations are given by C ( x ) = 5 , 000 + 2 x, R ( x ) = 10 x-. 001 x 2 , P ( x ) = R ( x )-C ( x ) , where the production output in 1 week is x radios. If production is increasing at the rate of 500 radios per week when producing is 2,000 radios, ļ¬nd the rate of increasing in (A) Cost, (B) Revenue (C) Proļ¬t? 2...
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lecture22 - If one travels north at 15 miles per hour and...

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