HW7 - Jolley Garrett Homework 7 Due Oct 9 2007 3:00 am Inst...

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Jolley, Garrett – Homework 7 – Due: Oct 9 2007, 3:00 am – Inst: R Heitmann 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. The due time is Central time. 001 (part 1 oF 1) 10 points ±ind the derivative oF f when f ( x ) = 3 x cos 5 x. 1. f 0 ( x ) = 3 cos 5 x + 15 x sin 3 x 2. f 0 ( x ) = 3 cos 5 x - 15 x sin 5 x correct 3. f 0 ( x ) = 15 cos 5 x + 5 x sin 5 x 4. f 0 ( x ) = 3 cos 3 x - 3 x sin 5 x 5. f 0 ( x ) = 15 cos 5 x - 3 x sin 5 x Explanation: Using the Formulas For the derivatives oF sine and cosine together with the Chain Rule we see that f 0 ( x ) = (3 x ) 0 cos 5 x + 3 x (cos 5 x ) 0 = 3 cos 5 x - 15 x sin 5 x. keywords: derivative, trig Function, chain rule 002 (part 1 oF 1) 10 points ±ind the value oF f 0 (0) when f ( x ) = (1 - 3 x ) - 5 . Correct answer: 15 . Explanation: Using the chain rule and the Fact that ( x α ) 0 = α x α - 1 , we obtain f 0 ( x ) = 15 (1 - 3 x ) 6 . At x = 0, thereFore, f 0 (0) = 15 . keywords: derivative, chain rule 003 (part 1 oF 1) 10 points ±ind f 0 ( x ) when f ( x ) = p x 2 - 4 x . 1. f 0 ( x ) = 1 2 ( x - 2) p x 2 - 4 x 2. f 0 ( x ) = x - 2 2 x 2 - 4 x 3. f 0 ( x ) = 2( x - 2) p x 2 - 4 x 4. f 0 ( x ) = ( x - 2) p x 2 - 4 x 5. f 0 ( x ) = x - 2 x 2 - 4 x correct 6. f 0 ( x ) = 2( x - 2) x 2 - 4 x Explanation: By the Chain Rule, f 0 ( x ) = 1 2 x 2 - 4 x (2 x - 4) . Consequently, f 0 ( x ) = x - 2 x 2 - 4 x . keywords: derivative, square root, chain rule 004 (part 1 oF 1) 10 points
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Jolley, Garrett – Homework 7 – Due: Oct 9 2007, 3:00 am – Inst: R Heitmann 2 Find f 0 ( x ) when f ( x ) = 1 x 2 - 8 x . 1. f 0 ( x ) = x - 4 (8 x - x 2 ) 1 / 2 2. f 0 ( x ) = 4 - x ( x 2 - 8 x ) 3 / 2 correct 3. f 0 ( x ) = 4 - x (8 x - x 2 ) 3 / 2 4. f 0 ( x ) = x - 4 (8 x - x 2 ) 3 / 2 5. f 0 ( x ) = x - 4 ( x 2 - 8 x ) 3 / 2 6. f 0 ( x ) = 4 - x ( x 2 - 8 x ) 1 / 2 Explanation: By the Chain Rule, f 0 ( x ) = - 1 2( x 2 - 8 x ) 3 / 2 (2 x - 8) . Consequently, f 0 ( x ) = 4 - x ( x 2 - 8 x ) 3 / 2 . keywords: derivative, square root, chain rule 005 (part 1 of 1) 10 points Determine f 0 ( x ) when f ( x ) = 1 - 2 x 1 - x 2 . 1. f 0 ( x ) = x - 2 (1 - x 2 ) 1 / 2 2. f 0 ( x ) = 2 + x (1 - x 2 ) 3 / 2 3. f 0 ( x ) = 2 + x (1 - x 2 ) 1 / 2 4. f 0 ( x ) = x - 2 (1 - x 2 ) 3 / 2 correct 5. f 0 ( x ) = 2 - x (1 - x 2 ) 3 / 2 6. f 0 ( x ) = 2 - x (1 - x 2 ) 1 / 2 Explanation: By the Product and Chain Rules, f 0 ( x ) = - 2 (1 - x 2 ) 1 / 2 + 2 x (1 - 2 x ) 2(1 - x 2 ) 3 / 2 = - 2(1 - x 2 ) + x (1 - 2 x ) (1 - x 2 ) 3 / 2 . Consequently,
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HW7 - Jolley Garrett Homework 7 Due Oct 9 2007 3:00 am Inst...

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