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Unformatted text preview: jiwani (amj566) – Homework05 – Fouli – (58395) 1 This printout should have 15 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 ) = 1 3 x 3 / 2 − 6 x 1 / 2 . 1. f ′ (4) = 0 2. f ′ (4) = 1 2 3. f ′ (4) = − 1 4. f ′ (4) = 1 5. f ′ (4) = − 1 2 correct Explanation: Since d dx x r = rx r − 1 , we see that f ′ ( x ) = 1 2 x 1 / 2 − 3 x − 1 / 2 . At x = 4, therefore, f ′ (4) = − 1 2 . 002 10.0 points Determine the derivative of f when f ( x ) = parenleftbigg 1 3 parenrightbigg 2 / 3 . 1. f ′ ( x ) = 2 9 x − 1 / 3 2. f ′ ( x ) = 0 correct 3. f ′ ( x ) = 2 3 parenleftbigg 1 3 parenrightbigg − 1 / 3 4. f ′ ( x ) = parenleftbigg 1 3 parenrightbigg x − 1 / 3 5. f ′ ( x ) does not exist 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 ) = 9 x 8 − 9 x − 3 − 2 . Correct answer: − 45. Explanation: Since ( x n ) ′ = n · x n − 1 , holds for all integers n , we see that f ′ ( x ) = 72 x 7 + 27 x − 4 . Hence f ′ ( − 1) = − 45 . 004 10.0 points Determine the derivative of f when f ( x ) = √ 3 x + 1 √ 3 x . 1. f ′ ( x ) = 1 2 parenleftbigg 3 x + 1 x √ 3 x parenrightbigg 2. f ′ ( x ) = 1 2 parenleftbigg 3 x − 1 √ 3 x parenrightbigg 3. f ′ ( x ) = 3 x + 1 x √ 3 x 4. f ′ ( x ) = 1 2 parenleftbigg 3 x − 1 x √ 3 x parenrightbigg correct jiwani (amj566) – Homework05 – Fouli – (58395) 2 5. f ′ ( x ) = 3 x + 1 √ 3 x 6. f ′ ( x ) = 3 x − 1 x √ 3 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 3 x − 1 2 1 x √ 3 x ....
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This note was uploaded on 07/10/2011 for the course KIN 321M taught by Professor Jensen during the Spring '11 term at University of Texas.
 Spring '11
 Jensen

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