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problem5_pdf - rabbani(tar547 Homework05 Fouli(58395 This...

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rabbani (tar547) – Homework05 – Fouli – (58395) 1 This print-out should have 15 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 + 2 x 1 / 2 . 1. f (4) = 11 2 correct 2. f (4) = 13 2 3. f (4) = 6 4. f (4) = 15 2 5. f (4) = 7 Explanation: Since d dx x r = rx r 1 , we see that f ( x ) = 5 2 x 1 / 2 + x 1 / 2 . At x = 4, therefore, f (4) = 11 2 . 002 10.0 points Determine the derivative of f when f ( x ) = parenleftbigg 2 3 parenrightbigg 2 / 3 . 1. f ( x ) = 0 correct 2. f ( x ) = 4 9 x 1 / 3 3. f ( x ) does not exist 4. f ( x ) = parenleftbigg 2 3 parenrightbigg x 1 / 3 5. f ( x ) = 2 3 parenleftbigg 2 3 parenrightbigg 1 / 3 Explanation: The derivative of any constant function is zero. Consequently, f ( x ) = 0 . 003 10.0 points Find the value of f ( 1) when f ( x ) = 2 x 3 7 x 2 5 . Correct answer: 8. Explanation: Since ( x n ) = n · x n 1 , holds for all integers n , we see that f ( x ) = 6 x 2 + 14 x 3 . Hence f ( 1) = 8 . 004 10.0 points Determine the derivative of f when f ( x ) = 5 x 1 5 x . 1. f ( x ) = 1 2 parenleftbigg 5 x 1 x 5 x parenrightbigg 2. f ( x ) = 1 2 parenleftbigg 5 x + 1 5 x parenrightbigg 3. f ( x ) = 5 x 1 5 x 4. f ( x ) = 5 x 1 x 5 x
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rabbani (tar547) – Homework05 – Fouli – (58395) 2 5. f ( x ) = 1 2 parenleftbigg 5 x + 1 x 5 x parenrightbigg correct 6. f ( x ) = 5 x + 1 x 5 x Explanation: Since d dx a x r = r a x r 1 for all exponents r negationslash = 0 and constants a , we see that f ( x ) = 1 2 radicalbigg 5 x + 1 2 1 x 5 x . After simplification this becomes f ( x ) = 1 2 parenleftbigg 5 x + 1 x 5 x parenrightbigg .
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