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Unformatted text preview: armington (kma786) – 5.3 – Stepp – (55860) 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 correct 3. 2 4 2 2 2 4. 2 4 2 2 2 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). armington (kma786) – 5.3 – Stepp – (55860) 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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 Spring '11
 STEPP
 Calculus, Derivative

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