Assignment 4-solutions

Assignment 4-solutions - nanni(arn437 Assignment 4...

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nanni (arn437) – Assignment 4 – guntel – (54940) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points 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 5. 2 4 - 2 2 - 2 correct 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).
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nanni (arn437) – Assignment 4 – guntel – (54940) 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 the graph of f we thus have to look at the sign of h
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