# P26 - concave up/down. What are the points of inﬂection?...

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Project 26 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! Examine the function h ( x ) = 3ln | x | x . What is the domain of h ( x )? Determine the horizontal asymptotes and vertical asymptotes, if any, for the graph of h ( x ). Does the function have any removable discontinuities? What are the intercepts for the graph of h ( x )? Does it display any symme- try? If so, what kind? Calculate h 0 ( x ). What critical numbers does h ( x ) have? Use a number line to determine the interval(s) on which the function is increasing/decreasing. What are the local extrema? Are they cusps or horizontal tangent lines? Calculate h 00 ( x ).

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Use a number line to determine the interval(s) on which the function is
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Unformatted text preview: concave up/down. What are the points of inﬂection? Separate a number line into the intervals on which h ( x ) is: • both increasing AND concave up • both increasing AND concave down • both decreasing AND concave up • both decreasing AND concave down and draw the basic shape of the curve on each interval. (There are four possibilities: each would be the left or right half of the shapes ∪ and ∩ .) Now piece your shapes together to draw the function h ( x ) below. Label all intercepts, local extrema, inﬂection points, removable discontinuities, and asymptotes....
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## This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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P26 - concave up/down. What are the points of inﬂection?...

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