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calculus homework 5

# calculus homework 5 - obiahu(vo879 HW05 Schultz(56395 This...

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obiahu (vo879) – HW05 – Schultz – (56395) 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 ) = 5 3 x 3 / 2 + 6 x 1 / 2 . 1. f (4) = 6 2. f (4) = 7 3. f (4) = 11 2 4. f (4) = 5 5. f (4) = 13 2 correct Explanation: Since d dx x r = rx r 1 , we see that f ( x ) = 5 2 x 1 / 2 + 3 x 1 / 2 . At x = 4, therefore, f (4) = 13 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 + 4 at which the tangent line is horizontal. 1. x -coord = 2 3 2. x -coords = 2 3 , 2 correct 3. x -coord = 2 4. x -coord = 2 3 5. x -coords = 2 3 , 2 6. x -coord = 2 Explanation: The tangent line will be horizontal at P ( x 0 , f ( x 0 )) when f ( x 0 ) = 0 . Now f ( x ) = 3 x 2 4 x 4 = (3 x + 2)( x 2) . Consequently, x 0 = 2 3 , 2 . 003 10.0 points Find the derivative of f when f ( x ) = x 7 2 + 2 x 3 2 1 x . 1. f ( x ) = 7 x 9 2 6 x 1 2 1 x 2 2. f ( x ) = 5 x 9 2 + 6 x 3 2 + 2 2 x 2 3. f ( x ) = 5 x 7 2 2 x 3 2 + 1 2 x 2 4. f ( x ) = 7 x 7 2 2 x 1 2 2 2 x 2 5. f ( x ) = 7 x 9 2 6 x 1 2 + 2 2 x 2 correct Explanation: Since d dx x r = rx r 1

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obiahu (vo879) – HW05 – Schultz – (56395) 2 holds for all real numbers r , we see that f ( x ) = 7 2 x 5 2 3 x 5 2 + 1 x 2 . To simplify this expression we bring the right hand side to a common denominator so that f ( x ) = 7 x 9 2 6 x 1 2 + 2 2 x 2 . 004 10.0 points Find the derivative of g ( x ) = parenleftbigg x + 2 x + 1 parenrightbigg (2 x 9) . 1. g ( x ) = 2 x 2 4 x 13 x + 1 2. g ( x ) = x 2 4 x + 13 x + 1 3. g ( x ) = 2 x 2 + 4 x + 13 ( x + 1) 2 correct 4. g ( x ) = 2 x 2 + 4 x + 13 x + 1 5. g ( x ) = 2 x 2 4 x 13 ( x + 1) 2 6. g ( x ) = x 2 + 4 x 13 ( x + 1) 2 Explanation: By the Quotient and Product Rules we see that g ( x ) = 2 braceleftbigg x + 2 x + 1 bracerightbigg + (2 x 9) braceleftbigg ( x + 1) ( x + 2) ( x + 1) 2 bracerightbigg = 2 braceleftbigg x + 2 x + 1 bracerightbigg + braceleftbigg 2 x 9 ( x + 1) 2 bracerightbigg = 2( x + 2)( x + 1) + (2 x 9) ( x + 1) 2 . But 2( x + 2)( x + 1) (2 x 9) = 2 x 2 + 4 x + 13 . Consequently g ( x ) = 2 x 2 + 4 x + 13 ( x + 1) 2 . 005 10.0 points Find the derivative of f when f ( x ) = x 3 x 4 x . 1. f ( x ) = 8 x (3 x 2 4) 2 2. f ( x ) = 8 x 3 x 2 4 3. f ( x ) = 1 3 + 4 x 2 4. f ( x ) = 8 x (3 x 2 4) 2 correct 5. f ( x ) = 1 3 4 x 2 6. f ( x ) = 8 x 3 x 4 Explanation: It’s best to simplify the function before dif- ferentiating: f ( x ) = x 2 3 x 2 4 .
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calculus homework 5 - obiahu(vo879 HW05 Schultz(56395 This...

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