HW8-solutions - wei(jw35975 – HW8 – milburn –(54685 1...

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Unformatted text preview: wei (jw35975) – HW8 – milburn – (54685) 1 This print-out should have 24 questions. Multiple-choice 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 ) = 3 x x- 3 x . 1. f ′ ( x ) = 18 x ( x 2- 3) 2 2. f ′ ( x ) =- 3 1- 3 x 2 3. f ′ ( x ) = 3 1 + 3 x 2 4. f ′ ( x ) = 18 x x 2- 3 5. f ′ ( x ) =- 18 x ( x 2- 3) 2 correct 6. f ′ ( x ) =- 18 x x- 3 Explanation: It’s best to simplify the function before dif- ferentiating: f ( x ) = 3 x 2 x 2- 3 . Then by the Quotient Rule, f ′ ( x ) = 6 x ( x 2- 3)- 2 x (3 x 2 ) ( x 2- 3) 2 Consequently, f ′ ( x ) =- 18 x ( x 2- 3) 2 . 002 10.0 points Find the derivative of f when f ( x ) = √ x ( x- 2) . 1. f ′ ( x ) = 2 x- 2 2 √ x 2. f ′ ( x ) = 2 x + 2 x √ x 3. f ′ ( x ) = 3 x + 2 x √ x 4. f ′ ( x ) = 2 x- 2 x √ x 5. f ′ ( x ) = 3 x + 2 2 √ x 6. f ′ ( x ) = 3 x- 2 2 √ x correct Explanation: By the Product Rule f ′ ( x ) = x- 2 2 √ x + √ x . After simplification this becomes f ′ ( x ) = x- 2 + 2 x 2 √ x = 3 x- 2 2 √ x . 003 10.0 points Find the value of f ′ (4) when f ( x ) = 4 3 x 3 / 2 + 2 x 1 / 2 . 1. f ′ (4) = 11 2 2. f ′ (4) = 4 3. f ′ (4) = 5 4. f ′ (4) = 9 2 correct 5. f ′ (4) = 6 Explanation: wei (jw35975) – HW8 – milburn – (54685) 2 Since d dx x r = rx r − 1 , we see that f ′ ( x ) = 2 x 1 / 2 + x − 1 / 2 . At x = 4, therefore, f ′ (4) = 9 2 . 004 10.0 points Find the derivative of g ( x ) = parenleftbigg x + 2 x + 3 parenrightbigg (2 x- 3) . 1. g ′ ( x ) = 2 x 2 + 12 x + 9 ( x + 3) 2 correct 2. g ′ ( x ) = x 2 + 12 x- 9 ( x + 3) 2 3. g ′ ( x ) = x 2- 12 x + 9 x + 3 4. g ′ ( x ) = 2 x 2- 12 x- 9 ( x + 3) 2 5. g ′ ( x ) = 2 x 2- 12 x- 9 x + 3 6. g ′ ( x ) = 2 x 2 + 12 x + 9 x + 3 Explanation: By the Quotient and Product Rules we see that g ′ ( x ) = 2 braceleftbigg x + 2 x + 3 bracerightbigg + (2 x- 3) braceleftbigg ( x + 3)- ( x + 2) ( x + 3) 2 bracerightbigg = 2 braceleftbigg x + 2 x + 3 bracerightbigg + braceleftbigg 2 x- 3 ( x + 3) 2 bracerightbigg = 2( x + 2)( x + 3) + (2 x- 3) ( x + 3) 2 . But 2( x + 2)( x + 3) + (2 x- 3) = 2 x 2 + 12 x + 9 . Consequently g ′ ( x ) = 2 x 2 + 12 x + 9 ( x + 3) 2 . 005 10.0 points Apply the Product Rule twice to determine the derivative of f when f ( x ) = ( x + 1)( x- 2)( x- 3) . 1. f ′ ( x ) = 3 x 2 + 4 x- 5 2. f ′ ( x ) = 3 x 2- 8 x + 1 correct 3. f ′ ( x ) = 3 x 2 + 8 x + 1 4. f ′ ( x ) = 3 x 2- 4 x- 5 5. f ′ ( x ) = ( x + 1)( x- 2) 6. f ′ ( x ) = ( x- 2)( x- 3) Explanation: Applying the Product Rule to f once we see that f ′ ( x ) = ( x- 2)( x- 3)+( x +1) d dx ( x- 2)( x- 3) ....
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This note was uploaded on 10/25/2011 for the course MATHEMATIC 408K taught by Professor Milburn during the Fall '11 term at University of Texas.

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HW8-solutions - wei(jw35975 – HW8 – milburn –(54685 1...

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