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# Exam3_2 7 - f will have a local extremum at the...

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Taylor, Douglas – Exam 3 – Due: Dec 5 2007, 1:00 am – Inst: JEGilbert 7 3. 4. correct 5. 6. Explanation: If F 1 and F 2 are anti-derivatives of f then F 1 ( x ) - F 2 ( x ) = constant independently of x ; this means that for any two anti-derivatives of f the graph of one is just a vertical translation of the graph of the other. In general, no horizontal translation of the graph of an anti-derivative can be the graph of an anti-derivative, nor can a hori- zontal and vertical translation be the graph of an anti-derivative. 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 anti-derivatives of f , therefore, we have to look more carefully at the actual graphs. But calculus ensures that (i) an anti-derivative of
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Unformatted text preview: f will have a local extremum at the x-intercepts of f . This eliminates two more Fgures since they contains graphs whose local extrema occur at points other than the x-intercepts of f . (ii) An anti-derivative of f is increasing on interval where the graph of f lies above the x-axis, and decreasing where the graph of f lies below the x-axis. Consequently, of the two remaining Fgures only consists entirely of graphs of anti-derivatives of f . keywords: antiderivative, graphical, graph, geometric interpretation 013 (part 1 of 1) 10 points A particle moving along a straight line has velocity v ( t ) = 5 sin t-6 cos t at time t . ±ind the position, s ( t ), of the particle at time t if initially s (0) = 2. (This is the mathematical model of Simple Harmonic Motion .)...
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