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Unformatted text preview: mao (tm23477) – HW5 – gualdani – (57180) 1 This printout should have 14 questions. Multiplechoice 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 8 x 1 / 2 . 1. f ′ (4) = 2 2. f ′ (4) = 3 correct 3. f ′ (4) = 7 2 4. f ′ (4) = 4 5. f ′ (4) = 5 2 Explanation: Since d dx x r = rx r − 1 , we see that f ′ ( x ) = 5 2 x 1 / 2 4 x − 1 / 2 . At x = 4, therefore, f ′ (4) = 3 . 002 10.0 points Determine the derivative of f when f ( x ) = parenleftbigg 1 2 parenrightbigg 2 / 3 . 1. f ′ ( x ) = 1 3 x − 1 / 3 2. f ′ ( x ) = parenleftbigg 1 2 parenrightbigg x − 1 / 3 3. f ′ ( x ) = 2 3 parenleftbigg 1 2 parenrightbigg − 1 / 3 4. f ′ ( x ) does not exist 5. f ′ ( x ) = 0 correct Explanation: The derivative of any constant function is zero. Consequently, f ′ ( x ) = 0 . 003 10.0 points Find the derivative of f ( x ) = ( x 2 + 3)(1 3 x 3 ) . 1. f ′ ( x ) = 2 x 2 27 x 3 15 x 4 2. f ′ ( x ) = 2 x 27 x 2 15 x 3 3. f ′ ( x ) = 2 x + 27 x 2 15 x 3 4. f ′ ( x ) = 2 x 27 x 2 15 x 4 correct 5. f ′ ( x ) = 2 x 2 + 27 x 3 15 x 4 Explanation: By the Product rule f ′ ( x ) = 2 x (1 3 x 3 ) 9 x 2 ( x 2 + 3) . Thus f ′ ( x ) = 2 x 27 x 2 15 x 4 . 004 10.0 points Find the derivative of f when f ( x ) = √ x (2 x 1) . 1. f ′ ( x ) = 6 x + 1 x √ x 2. f ′ ( x ) = 6 x 1 2 √ x correct mao (tm23477) – HW5 – gualdani – (57180) 2 3. f ′ ( x ) = 4 x + 1 x √ x 4. f ′ ( x ) = 4 x 1 x √ x 5. f ′ ( x ) = 6 x + 1 2 √ x 6. f ′ ( x ) = 4 x 1 2 √ x Explanation:...
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This note was uploaded on 05/12/2010 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.
 Fall '08
 schultz

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