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E2Review - MAC 2233 Review Exam 2 This is intended to be a...

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MAC 2233 Review – Exam 2 * This is intended to be a tool to help you review some of the material that could appear on the exam. It is not inclusive of all topics discussed in lecture. You should review problems from practice exams, problem sets, projects, and lecture as well. 1. Let s ( t ) = 32 t - 16 t 2 be the position at time t seconds of an object moving in a straight line. a) What is the average velocity of the object on the interval [ 2 , 4 ] ? b) Using limits, calculate the instantaneous velocity of the object at time t = 2 seconds. 2. If f (4) = 8 , g (4) = 2 , f ( - 4) = 1 , g ( - 4) = 3 , f 0 (4) = 10 , g 0 (4) = 12 , f 0 ( - 4) = 6 , and g 0 ( - 4) = - 2 , find H 0 (4) where H ( x ) = g ( f ( x ) - 3 x ) . 3. Suppose the total cost C ( x ) in dollars of producing x = 100 units of a product is $ 2000 and the marginal cost is $ 2 per unit. At what rate is the average cost C ( x ) of the items changing with respect to x (the marginal average cost)? 4. Suppose the depth W in inches of water within a certain retention pond during a storm is a function of the rainfall r in inches given by W ( r ) = 20 - 20 2 r + 1 . Suppose the rainfall after t hours is given by r ( t ) = t + t . Find the rate of change of the depth of the water with respect to time after t = 1 hour. 5. Find f 0 ( x ) for the functions: a) f ( x ) = x 2 5 - x 2 b) f ( x ) = (6 x - 2) 3 ( x + 4) 2 c) f ( x ) = x 1 3 + 4 x 2 3 At what x -values do these functions have horizontal tangent lines? Find the tangent line to each at x = 1 6. Find the value of a so that the tangent line to y = x 2 - 2 x +1
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