Solutions HW 5

Solutions HW 5 - mao(tm23477 HW5 gualdani(57180 This...

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mao (tm23477) – HW5 – gualdani – (57180) 1 This print-out should have 14 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 - 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

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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: By the Product Rule f ( x ) = 2 x - 1 2 x + 2 x .
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