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Unformatted text preview: moraboellstorff (erm823) 4.9 Arledge (55875) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points If the graph of f is which one of the following contains only graphs of antiderivatives of f ? 1. 2. 3. 4. 5. 6. cor rect Explanation: If F 1 and F 2 are antiderivatives of f then F 1 ( x ) F 2 ( x ) = constant independently of x ; this means that for any two antiderivatives of f the graph of one is just a vertical translation of the graph of the other. But no horizontal translation of the graph of an antiderivative of f will be moraboellstorff (erm823) 4.9 Arledge (55875) 2 the graph of an antiderivative of f , nor can a horizontal and vertical translation be the graph of an antiderivative. This rules out two sets of graphs. Now in each of the the remaining four fig ures the dotted and dashed graphs consist of vertical translations of the graph whose line style is a continuous line. To decide which of these figures consists of antiderivatives of f , therefore, we have to look more carefully at the actual graphs. But calculus ensures that (i) an antiderivative of f will have a local extremum at the xintercepts of f . This eliminates two more figures since they contains graphs whose local extrema occur at points other than the xintercepts of f . (ii) An antiderivative of f is increasing on interval where the graph of f lies above the xaxis, and decreasing where the graph of f lies below the xaxis. Consequently, of the two remaining figures only consists entirely of graphs of antiderivatives of f . keywords: antiderivative, graphical, graph, geometric interpretation 002 10.0 points A modern jet fighter aircraft needs to be travelling at 180 yards/sec down the runway in order to take off. It is known that the jet can accelerate from 0 to 180 yards/sec in 10 seconds (assume constant acceleration). Determine the shortest length the runway can be if the plane starts from rest at one end and has to take off at least 200 yards before the runway ends?...
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 Fall '10
 Alredge

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