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Unformatted text preview: jiwani (amj566) Review Exam 02 Fouli (58395) 1 This printout should have 32 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points The cost function for Levi Strauss to pro duce x pairs of blue jeans is C ( x ) = 1600 + 5 x 9 100 x 2 + 1 1250 x 3 . Find the marginal cost to Levi Strauss of producing 100 pairs of blue jeans. 1. marginal cost = $9 per pair 2. marginal cost = $10 per pair 3. marginal cost = $7 per pair 4. marginal cost = $8 per pair 5. marginal cost = $11 per pair correct Explanation: By definition, the Marginal cost is the derivative, C ( x ), of the cost function C ( x ). Now C ( x ) = 5 9 50 x + 3 1250 x 2 . When x = 100, therefore, marginal cost = C (100) = $11 per pair . 002 10.0 points TI has discovered that the total cost (in dollars) of producing x calculators per day is given by C ( x ) = 800 + 60 x x 2 5 . Find the Marginal Cost to TI at a production level of x calculators. 1. Marginal Cost = C ( x ) = 60 + 2 5 x 2. Marginal Cost = 60 + 1 5 x 3. Marginal Cost = C ( x ) x 4. Marginal Cost = C ( x + 1) C ( x ) 5. Marginal Cost = 60 1 5 x 6. Marginal Cost = C ( x ) = 60 2 5 x correct Explanation: The Marginal cost by definition is the derivative, C , of the Cost function C . Thus Marginal Cost = 60 2 5 x . 003 10.0 points Find the derivative of f when f ( x ) = 5 x cos 6 x . 1. f ( x ) = 5 cos5 x 5 x sin6 x 2. f ( x ) = 30 cos 6 x + 6 x sin 6 x 3. f ( x ) = 5 cos6 x 30 x sin 6 x correct 4. f ( x ) = 30 cos 6 x 5 x sin 6 x 5. f ( x ) = 5 cos6 x + 30 x sin 5 x Explanation: Using the formulas for the derivatives of sine and cosine together with the Chain Rule we see that f ( x ) = (5 x ) cos 6 x + 5 x (cos 6 x ) = 5 cos6 x 30 x sin 6 x . 004 10.0 points jiwani (amj566) Review Exam 02 Fouli (58395) 2 Find the derivative of f ( x ) = 3 x sin4 x + 3 4 cos 4 x . 1. f ( x ) = 12 x cos 4 x + 6 sin4 x 2. f ( x ) = 12 x cos 4 x 6 sin4 x 3. f ( x ) = 12 cos 4 x 4. f ( x ) = 12 x cos 4 x correct 5. f ( x ) = 12 x cos4 x Explanation: Since d dx sin x = cos x, d dx cos x = sin x, it follows that f ( x ) = 3 sin4 x + 12 x cos 4 x 3 sin 4 x. Consequently, f ( x ) = 12 x cos 4 x . 005 10.0 points Find the equation of the tangent line to the graph of 4 y 2 xy 9 = 0 , at the point P = (9 , 3). 1. 3 y = x 2. 14 y = 3 x + 15 3. 14 y + 3 x = 15 4. 5 y = x + 6 correct 5. 5 y + x = 6 Explanation: Differentiating implicitly with respect to x we see that 8 y dy dx y x dy dx = 0 , so dy dx = y 8 y x . At P = (9 , 3), therefore, dy dx vextendsingle vextendsingle vextendsingle P = 1 5 ....
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 Spring '11
 Jensen

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