105F04_Exam2_sh

105F04_Exam2_sh - Part I: Multiple Choice Questions (5...

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Part I: Multiple Choice Questions (5 Points Each) 1. Find the point on the curve y = x 3 - 3 x 2 + 3 x + 6 where the tangent line is horizontal. ( a ) x = - 1 ( b ) x = 0 ( c ) x = 1 ( d ) x = 2 ( e ) x = 3 2. Evaluate: lim h 0 x + h - x h ( a ) - 1 x 2 ( b ) 1 2 x ( c ) 1 x ( d ) - 1 x ( e ) Does not exist 3. If f ( x ) = x 2 + e 2 x then compute f 00 ( x ). ( a ) f 00 ( x ) = 2 + 4 e 2 x ( b ) f 00 ( x ) = 2 x + 2 e 2 x ( c ) f 00 ( x ) = 2 + e 2 x ( d ) f 00 ( x ) = 2 + (2 x - 1) e 2 x - 2 ( e ) f 00 ( x ) = e 2 x 4. The graph of the function f ( x ) is given in Figure 1 below. The points in the open interval ( - 1 , 8) where f ( x ) is not differentiable are: ( a ) 2 , 3 , 6 ( b ) 2 , 6 , 7 ( c ) 2 , 3 , 6 , 7 ( d ) - 1 , 1 , 5 ( e ) None y -1 0 1 2 3 4 6 7 8 x Figure 1 5. The revenue from the sale of 10,000 units of a certain item is 8,750 dollars, and the marginal revenue at that level is 0.64 dollars per unit. Use linear approximation to estimate the revenue if the sales level drops to 9,800 units. ( a
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This note was uploaded on 03/02/2012 for the course MATH 10250 taught by Professor Himonas during the Fall '08 term at Notre Dame.

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105F04_Exam2_sh - Part I: Multiple Choice Questions (5...

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