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Unformatted text preview: (There are four possibilities: each would be the left or right half of the shapes and .) Now try to piece your shapes together to make a rough freehand sketch of the function f ( x ) below. Label your cusps, horizontal tangents, and inection points. As one last experiment, use the second derivative test to verify the local extrema that you found. Do you have any critical numbers at which second derivative test cannot be used? 2. Suppose a particle moves in a straight line so that its position in feet at time t seconds is given by s ( t ) = t 2 et . How would you nd where the particle has its greatest speed (absolute value of velocity)? Find the greatest speed on [0 , 2]; on [2 , 4]. To what special type of point on the graph of s ( t ) do these correspond? Explain. .....
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 Fall '08
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 Calculus

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