Review for Exam #2 - jiwani (amj566) Review Exam 02 Fouli...

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Unformatted text preview: jiwani (amj566) Review Exam 02 Fouli (58395) 1 This print-out should have 32 questions. Multiple-choice 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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Review for Exam #2 - jiwani (amj566) Review Exam 02 Fouli...

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