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solution_c4pdf - armington(kma786 – 5.3 – Stepp...

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Unformatted text preview: armington (kma786) – 5.3 – Stepp – (55860) 1 This print-out should have 6 questions. Multiple-choice 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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solution_c4pdf - armington(kma786 – 5.3 – Stepp...

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