lecture17 - Lecture 17 1 Lecture 16, Part II and Lecture 17...

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Unformatted text preview: Lecture 17 1 Lecture 16, Part II and Lecture 17 (Sec. 3.6, 3.7) Related Rates ex. Water from a water heater is leaking onto the basement floor of a home. A circular puddle is cre- ated whose area is increasing at the rate of 25 square inches per minute. How fast is the radius of the pud- dle increasing when it is 10 inches? Lecture 17 2 RELATED RATES PROBLEMS: STEPS IN SOLVING 1) Assign variables to each quantity in the problem, and decide what rate you are trying to find. Then determine what rate(s) and information are given. Draw a sketch if possible. 2) Write an equation that relates the different vari- ables. 3) Implicitly differentiate your equation with respect to time. 4) Substitute the known quantities and solve for the desired rate of change. Lecture 17 3 ex. A department store estimates that weekly sales S and weekly advertising costs x are related by the equation S = 4000+60 x +0 . 02 x 2 . Right now weekly advertising costs are $2000, but these costs are rising at a rate of $8 per week. Find the rate at which the current weekly sales are changing with respect to time. Lecture 17...
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This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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lecture17 - Lecture 17 1 Lecture 16, Part II and Lecture 17...

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