hw 5 - silva (jrs4378) HW 05 gualdani (56455) 1 This...

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Unformatted text preview: silva (jrs4378) HW 05 gualdani (56455) 1 This print-out should have 21 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 (4) when f ( x ) = 1 3 x 3 / 2 + 2 x 1 / 2 . 1. f (4) = 5 2 2. f (4) = 3 3. f (4) = 7 2 4. f (4) = 2 5. f (4) = 3 2 correct Explanation: Since d dx x r = rx r 1 , we see that f ( x ) = 1 2 x 1 / 2 + x 1 / 2 . At x = 4, therefore, f (4) = 3 2 . 002 10.0 points Find the x-coordinate of all points on the graph of f ( x ) = x 3 2 x 2 4 x + 2 at which the tangent line is horizontal. 1. x-coords = 2 3 , 2 correct 2. x-coords = 2 3 , 2 3. x-coord = 2 3 4. x-coord = 2 5. x-coord = 2 3 6. x-coord = 2 Explanation: The tangent line will be horizontal at P ( x , f ( x )) when f ( x ) = 0 . Now f ( x ) = 3 x 2 4 x 4 = (3 x + 2)( x 2) . Consequently, x = 2 3 , 2 . 003 10.0 points Find the derivative of f when f ( x ) = 3 x 5 2 + 2 x 5 2 3 x . 1. f ( x ) = 15 x 7 2 10 x 3 2 3 x 2 2. f ( x ) = 15 x 7 2 10 x 3 2 + 6 2 x 2 correct 3. f ( x ) = 15 x 5 2 6 x 3 2 6 2 x 2 4. f ( x ) = 9 x 5 2 6 x 5 2 + 3 2 x 2 5. f ( x ) = 9 x 7 2 + 10 x 5 2 + 6 2 x 2 Explanation: Since d dx x r = rx r 1 silva (jrs4378) HW 05 gualdani (56455) 2 holds for all real numbers r , we see that f ( x ) = 15 2 x 3 2 5 x 7 2 + 3 x 2 . To simplify this expression we bring the right hand side to a common denominator so that f ( x ) = 15 x 7 2 10 x 3 2 + 6 2 x 2 . 004 10.0 points Find the derivative of g ( x ) = parenleftbigg x + 2 x + 1 parenrightbigg (2 x 7) . 1. g ( x ) = x 2 + 4 x 11 ( x + 1) 2 2. g ( x ) = 2 x 2 + 4 x + 11 x + 1 3. g ( x ) = x 2 4 x + 11 x + 1 4. g ( x ) = 2 x 2 + 4 x + 11 ( x + 1) 2 correct 5. g ( x ) = 2 x 2 4 x 11 ( x + 1) 2 6. g ( x ) = 2 x 2 4 x 11 x + 1 Explanation: By the Quotient and Product Rules we see that g ( x ) = 2 braceleftbigg x + 2 x + 1 bracerightbigg + (2 x 7) braceleftbigg ( x + 1) ( x + 2) ( x + 1) 2 bracerightbigg = 2 braceleftbigg x + 2 x + 1 bracerightbigg + braceleftbigg 2 x 7 ( x + 1) 2 bracerightbigg = 2( x + 2)( x + 1) + (2 x 7) ( x + 1) 2 . But 2( x + 2)( x + 1) (2 x 7) = 2 x 2 + 4 x + 11 ....
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This note was uploaded on 08/29/2010 for the course M 46455 taught by Professor Gualdani during the Spring '10 term at University of Texas at Austin.

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hw 5 - silva (jrs4378) HW 05 gualdani (56455) 1 This...

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