HW06-solutions - white (taw933) HW06 ben-zvi (55600) 1 This...

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Unformatted text preview: white (taw933) HW06 ben-zvi (55600) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the value of f (0) when f ( x ) = (1- 6 x ) 4 . Correct answer: 24. Explanation: Using the chain rule and the fact that ( x ) = x 1 , we obtain f ( x ) = 24 (1- 6 x ) 5 . At x = 0, therefore, f (0) = 24 . 002 10.0 points Find the derivative of f when f ( x ) = sin(cos x ) . 1. f ( x ) = cos x sin(sin x ) 2. f ( x ) = cos x sin(cos x ) 3. f ( x ) =- sin x cos(sin x ) 4. f ( x ) =- cos x sin(cos x ) 5. f ( x ) = sin x cos(cos x ) 6. f ( x ) =- sin x cos(cos x ) correct Explanation: Using the Chain Rule we see that f ( x ) = parenleftBig cos(cos x ) parenrightBig (- sin x ) =- sin x cos(cos x ) . 003 10.0 points Find the derivative of f when f ( x ) = parenleftBig 2 x 7 / 2- 3 x 7 / 2 parenrightBig 2 . 1. f ( x ) = 7 parenleftbigg 4 x 14- 9 x 8 parenrightbigg correct 2. f ( x ) = 8 parenleftbigg 4 + 3 x 14 x 7 parenrightbigg 3. f ( x ) = 7 parenleftbigg 2 x 7 + 3 x 7 parenrightbigg 4. f ( x ) = 8 parenleftbigg 4- 3 x 14 x 7 parenrightbigg 5. f ( x ) = 8 parenleftbigg 4 x 14 + 9 x 8 parenrightbigg 6. f ( x ) = 7 parenleftbigg 2 x 14- 3 x 7 parenrightbigg Explanation: After expansion, parenleftBig 2 x 7 / 2- 3 x 7 / 2 parenrightBig 2 = 4 x 7- 12 + 9 x 7 Thus f ( x ) = 28 x 6- 63 x 8 = 28 x 6- 63 x 8 . Consequently, f ( x ) = 7 parenleftbigg 4 x 6- 9 x 8 parenrightbigg = 7 parenleftbigg 4 x 14- 9 x 8 parenrightbigg . 004 10.0 points Find the x- and y-intercepts of the tangent line to the graph of y = ( 3 x + 5 ) 1 / 3 at the point (1 , 2). white (taw933) HW06 ben-zvi (55600) 2 1. x-intercept =- 5 3 , y-intercept = 5 12 2. x-intercept =- 20 3 , y-intercept = 11 6 3. x-intercept =- 6 , y-intercept = 3 2 4. x-intercept =- 7 , y-intercept = 7 4 correct 5. x-intercept =- 21 4 , y-intercept = 7 4 Explanation: By the power rule, dy dx = ( 3 x + 5 ) 1 / 3 1 ....
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This note was uploaded on 12/05/2011 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

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HW06-solutions - white (taw933) HW06 ben-zvi (55600) 1 This...

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