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Unformatted text preview: moraboellstorff (erm823) 5.3 Arledge (55875) 1 This printout should have 6 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A function h has graph 2 4 2 2 4 on ( 3 , 4). If f ( x ) = integraldisplay x 2 h ( t ) dt, ( x  2) , which of the following is the graph of f on ( 3 , 4)? 1. 2 4 2 2 2 2. 2 4 2 2 2 3. 2 4 2 2 2 4. 2 4 2 2 2 correct 5. 2 4 2 2 2 6. 2 4 2 2 2 Explanation: Since f ( x ) is defined only for x  2, there will be no graph of f on the interval ( 3 , 2). moraboellstorff (erm823) 5.3 Arledge (55875) 2 This already eliminates two of the possible graphs. On the other hand, f ( 2) = integraldisplay 2 2 h ( x ) dx = 0 , eliminating two more graphs. Finally, by the Fundamental Theorem of Calculus, f ( x ) = h ( x ) on ( 2 , 4), so f ( x ) will be increasing on any interval on which h > 0, and decreasing on any interval on which h < 0. To determine which of the remaining two possible graphs is...
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This note was uploaded on 02/02/2011 for the course M 408 S taught by Professor Alredge during the Fall '10 term at University of Texas at Austin.
 Fall '10
 Alredge

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