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Unformatted text preview: Lecture 14 1 Lecture 14: (Sec. 3.3 and 3.4, part I) Chain Rule, part II; Marginals ex. A store sells a CD for $16. If daily sales x are increasing by three CDs per day, what is the rate at which revenue is increasing with respect to time? Lecture 14 2 Chain Rule: Rate of Change Version Let y be a differentiable function of u where u is a differentiable function of x . Then y is a differentiable function of x and ex. Suppose y = 4 u + 1 u and u = x 2 3. Find dy dx . What is the slope of the tangent line to y = f ( x ) when x = 1? Lecture 14 3 Marginal Functions in Economics ex. Let C ( x ) = 1000 + 25 x . 1 x 2 be the cost function for a product. 1) Find the rate at which cost is changing with re spect to x for a production level of 100 units. 2) Find the actual cost of producing the 101st unit. ( C (101) = 1000 + 25(101) . 1(101) 2 = $2504 . 90). Lecture 14 4 To see why this is so, let C ( x ) be a cost function and consider the graph: Lecture 14 5 Marginals If C ( x ) = the total cost of producing...
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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.
 Spring '08
 Smith
 Calculus, Chain Rule

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