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Unformatted text preview: white (taw933) HW05 benzvi (55600) 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 xcoordinates of all the points on the graph of f ( x ) = 2 x 3 + 2 x 2 2 x + 4 at which the tangent line is horizontal. 1. xcoord = 1 3 , 1 2. xcoord = 1 3 3. xcoords = 1 3 , 1 4. xcoord = 1 3 5. xcoords = 1 , 1 3 correct 6. xcoord = 1 Explanation: The tangent line will be horizontal at P ( x , f ( x )) when f ( x ) = 0 . Now f ( x ) = 6 x 2 + 4 x 2 = 2(3 x 1)( x + 1) . Consequently, x = 1 , 1 3 . 002 10.0 points Find the value of f (1) when f ( x ) = 9 x 1 6 + 8 x 1 6 + 8 . Correct answer: 0 . 166667. Explanation: Since ( x r ) = r x r 1 holds for all real numbers r , we see that f ( x ) = 3 2 x 5 6 4 3 x 7 6 . Hence f (1) = 1 6 . 003 10.0 points Find the derivative of g ( x ) = parenleftbigg x + 3 x + 2 parenrightbigg (2 x 9) . 1. g ( x ) = x 2 8 x + 21 x + 2 2. g ( x ) = 2 x 2 8 x 21 ( x + 2) 2 3. g ( x ) = x 2 + 8 x 21 ( x + 2) 2 4. g ( x ) = 2 x 2 + 8 x + 21 x + 2 5. g ( x ) = 2 x 2 + 8 x + 21 ( x + 2) 2 correct 6. g ( x ) = 2 x 2 8 x 21 x + 2 Explanation: By the Quotient and Product Rules we see that g ( x ) = 2 braceleftbigg x + 3 x + 2 bracerightbigg + (2 x 9) braceleftbigg ( x + 2) ( x + 3) ( x + 2) 2 bracerightbigg = 2 braceleftbigg x + 3 x + 2 bracerightbigg + braceleftbigg 2 x 9 ( x + 2) 2 bracerightbigg = 2( x + 3)( x + 2) + (2 x 9) ( x + 2) 2 . white (taw933) HW05 benzvi (55600) 2 But 2( x + 3)( x + 2) (2 x 9) = 2 x 2 + 8 x + 21 . Consequently g ( x ) = 2 x 2 + 8 x + 21 ( x + 2) 2 . 004 10.0 points Find the derivative of f when f ( x ) = 4 x 3 + 3 x 2 + 4 . 1. f ( x ) = 6 parenleftBig 2 x 5 + 1 x 3 parenrightBig 2. f ( x ) = 6 parenleftBig 2 x 5 1 x 3 parenrightBig correct 3. f ( x ) = 2 parenleftBig 2 x 4 + 1 x 2 parenrightBig 4. f ( x ) = 6 parenleftBig 1 2 x 5 x 3 parenrightBig 5. f ( x ) = 2 parenleftBig 2 x 4 1 x 2 parenrightBig 6. f ( x ) = 2 parenleftBig 1 2 x 5 x 3 parenrightBig 7. none of the other answers Explanation: Since d dx ( x r ) = rx r 1 holds for all r , we see that f ( x ) = 12 x 2 6 x 3 . Consequently, f ( x ) = 6 parenleftBig 2 x 5 1 x 3 parenrightBig . keywords: derivatives, negative powers 005 10.0 points Find the derivative of f when f ( x ) = x x + 1 x ....
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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.
 Spring '08
 schultz
 Real Numbers, Differential Calculus

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