EXAM2.pdf - young(toy68 EXAM2 villafuerte altu(53780 This...

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young (toy68) – EXAM2 – villafuerte altu – (53780) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Find the x -coordinate of all points on the graph of f ( x ) = x 3 - 4 x 2 - 16 x + 3 at which the tangent line is horizontal. 1. x -coord = 4 3 2. x -coord = 4 3. x -coords = 4 3 , - 4 4. x -coords = - 4 3 , 4 correct 5. x -coord = - 4 3 6. x -coord = - 4 Explanation: The tangent line will be horizontal at P ( x 0 , f ( x 0 )) when f ( x 0 ) = 0 . Now f ( x ) = 3 x 2 - 8 x - 16 = (3 x + 4)( x - 4) . Consequently, x 0 = - 4 3 , 4 . 002 10.0points Find the derivative of f when f ( x ) = x 3 x + 1 x . 1. f ( x ) = 1 3 + 1 x 2 2. f ( x ) = - 2 x (3 x 2 + 1) 2 3. f ( x ) = 2 x 3 x 2 + 1 4. f ( x ) = 2 x (3 x 2 + 1) 2 correct 5. f ( x ) = 1 3 - 1 x 2 6. f ( x ) = - 2 x 3 x + 1 Explanation: It’s best to simplify the function before dif- ferentiating: f ( x ) = x 2 3 x 2 + 1 . Then by the Quotient Rule, f ( x ) = 2 x (3 x 2 + 1) - 6 x ( x 2 ) (3 x 2 + 1) 2 Consequently, f ( x ) = 2 x (3 x 2 + 1) 2 . 003 10.0points Find the value of F (3) when F ( x ) = f ( x ) f ( x ) - g ( x ) and f (3) = 4 , f (3) = 3 , g (3) = 1 , g (3) = 2 . 1. F (3) = - 11 9 2. F (3) = 5 9 correct 3. F (3) = 2 9 4. F (3) = - 5 9
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young (toy68) – EXAM2 – villafuerte altu – (53780) 2 5. F (3) = 11 9 Explanation: By the Quotient Rule, F ( x ) = f ( x ) ( f ( x ) - g ( x )) - f ( x ) ( f ( x ) - g ( x )) ( f ( x ) - g ( x )) 2 = f ( x ) g ( x ) - f ( x ) g ( x ) ( f ( x ) - g ( x )) 2 , Consequently, F (3) = 5 9 . 004 10.0points Recently, Stewart drove the 120 kms from Austin to San Antonio, leaving at 12noon and arriving in SA at 1:30pm. He stayed briefly and then started back. The GPS system in his car recorded his distance from Austin and the time elapsed. It plotted these accurately to scale on the following graph: time kms 20 40 60 80 100 120 12:30 1:00 1:30 2:00 distance travelled being plotted on the y -axis and time elapsed on the x -axis where 1 unit in y -direction = 10 kms and 1 unit in x -direction = 10 minutes. Consider the following statements: A. His average speed between 1:10pm and 1:20pm wasmorethan 120 kms/hr. B. At 1:00pm hewasaccelerating . C. At 12:50pm he was stationary momen- tarily . Which of these are correct? 1. all of them correct 2. C only 3. B and C only 4. A and C only 5. B only 6. none of them 7. A and B only 8. A only Explanation: A. True: he travelled 40 kms in those 10 minutes.
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