review3s11

# review3s11 - MAC 2311 Test Three Review, Spring 2011 Exam...

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MAC 2311 Test Three Review, Spring 2011 Exam covers Lectures 17 { 24, Chapter 3, Sec. 17 { Chapter 4, Sec. 24 1. Find f 0 ( x ) for the following: a) f ( x ) = log 4 ( x cos x ) 2 b) y = e tan x x c) y = 3 x 3 +2 x d) y = x sin x e) f ( x ) = sin ¡ 1 x 5 · 2. Use logarithmic diﬁerentiation to ﬂnd f 0 ( x ) for the following: a) f ( x ) = (6 x ¡ 2) 3 ( x + 4) 2 b) f ( x ) = e x ¡ 3 3 p 6 + 3 x (3 x + 1) 2 3. a) Use implicit diﬁerentiation to ﬂnd f 0 ( x ) if f ( x ) = cos ¡ 1 x . b) If x = cos y , ﬂnd y 00 . 4. The position of an object at time t (in seconds) is given by s ( t ) = 2 t 3 ¡ 15 t 2 +24 t where s is measured in feet. Find: a) the times at which the object is at rest b) the time intervals on which the object is moving in a positive direction c) the displacement and total distance traveled by the object in the ﬂrst 4 seconds d) the intervals on which the object is speeding up and slowing down 5. Suppose that the cost function for a product is C ( x ) = 1 : 25 x 2 +25 x +8000 : Then average cost is given by C ( x ) x . Find and interpret the marginal cost and marginal average cost at a production level of 50 units. 6. The demand function for a product is p ( x ) = 45 ¡ p x 2 where p is the price at which x items will sell. If the total revenue R ( x ) = xp , ﬂnd the marginal revenue when 1600 items are produced. Now suppose

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## This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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review3s11 - MAC 2311 Test Three Review, Spring 2011 Exam...

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