HW05-solutions

# HW05-solutions - le(chl528 – HW05 – seckin –(57195 1...

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Unformatted text preview: le (chl528) – HW05 – seckin – (57195) 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 ) = x 3 / 2- 4 x 1 / 2 . 1. f ′ (4) = 7 2 2. f ′ (4) = 4 3. f ′ (4) = 2 correct 4. f ′ (4) = 5 2 5. f ′ (4) = 3 Explanation: Since d dx x r = rx r − 1 , we see that f ′ ( x ) = 3 2 x 1 / 2- 2 x − 1 / 2 . At x = 4, therefore, f ′ (4) = 2 . 002 10.0 points Determine the derivative of f when f ( x ) = parenleftbigg 1 5 parenrightbigg 2 / 3 . 1. f ′ ( x ) does not exist 2. f ′ ( x ) = 0 correct 3. f ′ ( x ) = 2 3 parenleftbigg 1 5 parenrightbigg − 1 / 3 4. f ′ ( x ) = 2 15 x − 1 / 3 5. f ′ ( x ) = parenleftbigg 1 5 parenrightbigg x − 1 / 3 Explanation: The derivative of any constant function is zero. Consequently, f ′ ( x ) = 0 . 003 10.0 points Find the derivative of f ( x ) = ( x 5 + 2)(1- 3 x 2 ) . 1. f ′ ( x ) = 5 x 5 + 12 x 2- 21 x 6 2. f ′ ( x ) = 5 x 5- 12 x 2- 21 x 6 3. f ′ ( x ) = 5 x 4 + 12 x- 21 x 5 4. f ′ ( x ) = 5 x 4- 12 x- 21 x 5 5. f ′ ( x ) = 5 x 4- 12 x- 21 x 6 correct Explanation: By the Product rule f ′ ( x ) = 5 x 4 (1- 3 x 2 )- 6 x ( x 5 + 2) . Thus f ′ ( x ) = 5 x 4- 12 x- 21 x 6 . 004 10.0 points Find the derivative of f when f ( x ) = √ x (2 x- 1) . 1. f ′ ( x ) = 6 x- 1 2 √ x correct 2. f ′ ( x ) = 4 x- 1 x √ x le (chl528) – HW05 – seckin – (57195) 2 3. f ′ ( x ) = 4 x- 1 2 √ x 4. f ′ ( x ) = 6 x + 1 2 √ x 5. f ′ ( x ) = 6 x + 1 x √ x 6. f ′ ( x ) = 4 x + 1 x √ x Explanation: By the Product Rule...
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HW05-solutions - le(chl528 – HW05 – seckin –(57195 1...

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