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 – find all choices before answering. 001 10.0points Find 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 10.0points 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 differentiation and the rule ( x n ) = n · x n 1 , we see that f ( x ) = 48 x 7 + 21 x 2 . 003 10.0points Determine the derivative of f when f ( x ) = parenleftbigg 2 5 parenrightbigg 2 / 3 . 1. f ( x ) does not exist 2. f ( x ) = 0 correct 3. f ( x ) = 4 15 x 1 / 3 4. f ( x ) = parenleftbigg 2 5 parenrightbigg x 1 / 3 5. f ( x ) = 2 3 parenleftbigg 2 5 parenrightbigg 1 / 3 Explanation: The derivative of any constant function is zero. Consequently, f ( x ) = 0 .
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wei (jw35975) – HW7 – milburn – (54685) 2 004 10.0points Find the x -coordinates of all the points on the graph of f ( x ) = x 3 + 4 x 2 16 x + 5 at which the tangent line is horizontal.
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