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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 π 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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 Spring '08
 Smith
 Calculus, Inch, actual change

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