HW7-solutions - wei(jw35975 HW7 milburn(54685 This...

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wei (jw35975) – HW7 – milburn – (54685) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ind the derivative oF f ( x ) = x + 2 x . 1. f ( x ) = x 2 x x 2. f ( x ) = x + 2 x 3. f ( x ) = x + 2 x x 4. f ( x ) = x 2 2 x x correct 5. f ( x ) = x 2 2 x 6. f ( x ) = x + 2 2 x x Explanation: Since d dx x = d dx x 1 / 2 = 1 2 x 1 / 2 = 1 2 x , while d dx 1 x = d dx x 1 / 2 = 1 2 x 3 / 2 = 1 2 x x . Thus f ( x ) = 1 2 x 1 x x . Consequently, f ( x ) = x 2 2 x x . 002 10.0 points Determine f ( x ) when f ( x ) = 6 x 8 + 7 x 3 + 5 π. 1. f ( x ) = 48 x 7 + 21 x 2 + 5 π 2. f ( x ) = 6 x 8 + 21 x 2 + 5 3. f ( x ) = 48 x 7 + 21 x 2 + 5 πx 4. f ( x ) = 48 x 7 + 21 x 2 correct 5. f ( x ) = 48 x 7 + 7 x 3 Explanation: By linearity oF di²erentiation and the rule ( x n ) = n · x n 1 , we see that f ( x ) = 48 x 7 + 21 x 2 . 003 10.0 points Determine the derivative oF f when f ( x ) = p 2 5 P 2 / 3 . 1. f ( x ) does not exist 2. f ( x ) = 0 correct 3. f ( x ) = 4 15 x 1 / 3 4. f ( x ) = p 2 5 P x 1 / 3 5. f ( x ) = 2 3 p 2 5 P 1 / 3 Explanation: The derivative oF any constant Function is zero. Consequently, f ( x ) = 0 .
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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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HW7-solutions - wei(jw35975 HW7 milburn(54685 This...

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