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# HW 6 - Tran Tony Homework 6 Due Oct 2 2007 3:00 am Inst...

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Tran, Tony – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: Samuels 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 ) = 1 2 2 / 3 . 1. f 0 ( x ) = 1 2 x - 1 / 3 2. f 0 ( x ) = 1 3 x - 1 / 3 3. f 0 ( x ) = 2 3 1 2 - 1 / 3 4. f 0 ( x ) does not exist 5. f 0 ( x ) = 0 correct Explanation: The derivative of any constant function is zero. Consequently, f 0 ( 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 ) = 2 x 3 + 8 x 2 - 32 x + 3 . 1. x -coords = - 4 3 , 4 2. x -coord = 4 3 3. x -coord = 4 4. x -coord = - 4 3 5. x -coords = 4 3 , - 4 correct 6. x -coord = - 4 Explanation: The tangent line will be horizontal at P ( x 0 , f ( x 0 )) when f 0 ( x 0 ) = 0 . Now f 0 ( x ) = 6 x 2 + 16 x - 32 = 2(3 x - 4)( x + 4) . Consequently, x 0 = 4 3 , - 4 . keywords: horizontal tangent line, extrema, polynomials, derivative 003 (part 1 of 1) 10 points Differentiate the function f ( x ) = 5 x 3 1. df dx = - 3 5 x 4 correct 2. df dx = - 5 3 x 2 3. df dx = 4 5 x 4 4. df dx = 3 5 x 2 5. df dx = 3 5 x 4 Explanation: f ( x ) = 5 x 3 = 5 x - 3 f 0 ( x ) = - 3 5 x - 4 = - 3 5 x 4

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Tran, Tony – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: Samuels 2 keywords: derivative, rational function 004 (part 1 of 1) 10 points Find the derivative of f ( x ) = ( x 5 + 2)(1 - 2 x 3 ) . 1. f 0 ( x ) = 5 x 5 - 12 x 3 - 16 x 7 2. f 0 ( x ) = 5 x 5 + 12 x 3 - 16 x 7 3. f 0 ( x ) = 5 x 4 - 12 x 2 - 16 x 6 4. f 0 ( x ) = 5 x 4 - 12 x 2 - 16 x 7 correct 5. f 0 ( x ) = 5 x 4 + 12 x 2 - 16 x 6 Explanation: By the Product rule f 0 ( x ) = 5 x 4 (1 - 2 x 3 ) - 6 x 2 ( x 5 + 2) . Thus f 0 ( x ) = 5 x 4 - 12 x 2 - 16 x 7 . keywords: derivatives, product rule 005 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = x ( x - 2) . 1. f 0 ( x ) = 3 x + 2 x x 2. f 0 ( x ) = 2 x - 2 x x 3. f 0 ( x ) = 2 x + 2 x x 4. f 0 ( x ) = 3 x + 2 2 x 5. f 0 ( x ) = 2 x - 2 2 x 6. f 0 ( x ) = 3 x - 2 2 x correct Explanation: By the Product Rule f 0 ( x ) = x - 2 2 x + x . After simplification this becomes f 0 ( x ) = x - 2 + 2 x 2 x = 3 x - 2 2 x . keywords: derivatives, product rule 006 (part 1 of 1) 10 points Find f 0 ( x ) when f ( x ) = 4 x - 1 5 x - 1 . 1. f 0 ( x ) = - 1 (5 x - 1) 2 2. f 0 ( x ) = 5 - 4 x (5 x - 1) 2 3. f 0 ( x ) = 1 5 x - 1 4. f 0 ( x ) = 20 x - 4 (5 x - 1) 2 5. f 0 ( x ) = 1 (5 x - 1) 2 correct Explanation: Using the Quotient Rule for differentiation we see that f 0 ( x ) = 4(5 x - 1) - 5(4 x - 1) (5 x - 1) 2 .
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HW 6 - Tran Tony Homework 6 Due Oct 2 2007 3:00 am Inst...

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