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Homework 6 - Garcia Ilse – Homework 6 – Due Oct 2 2007...

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Unformatted text preview: Garcia, Ilse – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: Fonken 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Determine the derivative of f when f ( x ) = µ 4 5 ¶ 2 / 3 . 1. f ( x ) = 2 3 µ 4 5 ¶- 1 / 3 2. f ( x ) does not exist 3. f ( x ) = 8 15 x- 1 / 3 4. f ( x ) = 0 correct 5. f ( x ) = µ 4 5 ¶ x- 1 / 3 Explanation: The derivative of any constant function is zero. Consequently, f ( x ) = 0 . keywords: derivative, constant function 002 (part 1 of 1) 10 points Find the x-coordinates of all the points on the graph of f at which the tangent line is horizontal when f ( x ) = x 3 + x 2- x + 5 . 1. x-coord =- 1 3 2. x-coord = 1 3. x-coords =- 1 3 , 1 4. x-coord =- 1 5. x-coord = 1 3 6. x-coords = 1 3 ,- 1 correct Explanation: The tangent line will be horizontal at P ( x ,f ( x )) when f ( x ) = 0 . Now f ( x ) = 3 x 2 + 2 x- 1 = (3 x- 1)( x + 1) . Consequently, x = 1 3 ,- 1 . keywords: horizontal tangent line, extrema, polynomials, derivative 003 (part 1 of 1) 10 points Differentiate the function f ( x ) = √ 7 x 8 1. df dx =- 8 √ 7 x 7 2. df dx =- 8 √ 7 x 9 correct 3. df dx = √ 7 8 x 7 4. df dx = 8 √ 7 x 9 5. df dx =- 9 √ 7 x 9 Explanation: f ( x ) = √ 7 x 8 = √ 7 x- 8 f ( x ) =- 8 √ 7 x- 9 =- 8 √ 7 x 9 Garcia, Ilse – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: Fonken 2 keywords: derivative, rational function 004 (part 1 of 1) 10 points Find the derivative of f ( x ) = ( x 3 + 1)(1- 2 x 2 ) . 1. f ( x ) = 3 x 2- 4 x- 10 x 3 2. f ( x ) = 3 x 3 + 4 x 2- 10 x 4 3. f ( x ) = 3 x 3- 4 x 2- 10 x 4 4. f ( x ) = 3 x 2 + 4 x- 10 x 3 5. f ( x ) = 3 x 2- 4 x- 10 x 4 correct Explanation: By the Product rule f ( x ) = 3 x 2 (1- 2 x 2 )- 4 x ( x 3 + 1) . Thus f ( x ) = 3 x 2- 4 x- 10 x 4 . keywords: derivatives, product rule 005 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = √ x (2 x + 1) . 1. f ( x ) = 6 x- 1 2 √ x 2. f ( x ) = 4 x + 1 x √ x 3. f ( x ) = 6 x + 1 2 √ x correct 4. f ( x ) = 6 x- 1 x √ x 5. f ( x ) = 4 x- 1 x √ x 6. f ( x ) = 4 x + 1 2 √ x Explanation: By the Product Rule f ( x ) = 2 x + 1 2 √ x + 2 √ x. After simplification this becomes f ( x ) = 2 x + 1 + 4 x 2 √ x = 6 x + 1 2 √ x ....
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Homework 6 - Garcia Ilse – Homework 6 – Due Oct 2 2007...

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