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Unformatted text preview: Garcia, Ilse – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: Fonken 1 This printout should have 20 questions. Multiplechoice 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 xcoordinates 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. xcoord = 1 3 2. xcoord = 1 3. xcoords = 1 3 , 1 4. xcoord = 1 5. xcoord = 1 3 6. xcoords = 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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 Spring '08
 schultz
 Derivative

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