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Unformatted text preview: Version 028 Exam 2 Helleloid (58250) 1 This printout should have 19 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the derivative of f when f ( x ) = 4 x cos6 x . 1. f ( x ) = 4 cos 4 x 4 x sin 6 x 2. f ( x ) = 4 cos 6 x 24 x sin6 x correct 3. f ( x ) = 4 cos 6 x + 24 x sin4 x 4. f ( x ) = 24 cos 6 x 4 x sin6 x 5. f ( x ) = 24 cos 6 x + 6 x sin6 x Explanation: Using the formulas for the derivatives of sine and cosine together with the Chain Rule we see that f ( x ) = (4 x ) cos 6 x + 4 x (cos 6 x ) = 4 cos 6 x 24 x sin6 x . 002 10.0 points Determine the derivative of f ( x ) = x x 1 . 1. f ( x ) = 2 + 3 x 2 x 1 2. f ( x ) = 3 x 2 2 x 1 correct 3. f ( x ) = 2 3 x 2 x 1 4. f ( x ) = 2 3 x x 1 5. f ( x ) = 3 x 2 x 1 6. f ( x ) = 2 + 3 x x 1 Explanation: By the Product and Chain Rules, f ( x ) = x 1+ x 2 x 1 = 2( x 1) + x 2 x 1 . Consequently, f ( x ) = 3 x 2 2 x 1 . keywords: 003 10.0 points Find the second derivative of f when f ( x ) = cos 2 x 3 sin 2 x . 1. f ( x ) = 5 cos2 x 2. f ( x ) = 10 sin2 x 3. f ( x ) = 10 cos2 x correct 4. f ( x ) = 5 sin2 x 5. f ( x ) = 5 cos2 x 6. f ( x ) = 10 cos2 x Explanation: Differentiating once we see that f ( x ) = 2 sin 2 x 6 sin x cos x . Now 2 sin x cos x = sin 2 x , so f ( x ) = 5 sin 2 x . Consequently, by differentiating once again we obtain f ( x ) = 10 cos 2 x . Version 028 Exam 2 Helleloid (58250) 2 keywords: second derivative, trig function 004 10.0 points Find the equation of the tangent line to the graph of y 2 xy 15 = 0 , at the point P = (2 , 5). 1. 8 y + 5 x = 30 2. 7 y = 5 x + 25 3. 2 y = 5 x 4. 8 y = 5 x + 30 correct 5. 7 y + 5 x = 25 Explanation: Differentiating implicitly with respect to x we see that 2 y dy dx y x dy dx = 0 , so dy dx = y 2 y x . At P = (2 , 5), therefore, dy dx vextendsingle vextendsingle vextendsingle P = 5 8 . Thus by the point slope formula, the equation of the tangent line at P is given by y 5 = 5 8 ( x 2) . Consequently, 8 y = 5 x + 30 . 005 10.0 points The cost function for Levi Strauss to pro duce x pairs of blue jeans is C ( x ) = 4700 + 7 x 1 50 x 2 + 3 5000 x 3 . Find the marginal cost to Levi Strauss of producing 100 pairs of blue jeans. 1. marginal cost = $22 per pair 2. marginal cost = $21 per pair correct 3. marginal cost = $25 per pair 4. marginal cost = $24 per pair 5. marginal cost = $23 per pair Explanation: By definition, the Marginal cost is the derivative, C ( x ), of the cost function C ( x )....
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This note was uploaded on 12/04/2009 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.
 Fall '08
 schultz
 Calculus

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