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# P23 - • both decreasing AND concave up • both...

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Project 22/23 MAC 2233 1. Examine the function h ( x ) = 27 x 2 x ( x + 1) 3 . What is its domain ? 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 of the graph of h ( x ) ? Calculate h 0 ( x ) , and 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 ) . Use a number line to determine the interval(s) on which the function is 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

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Unformatted text preview: • both decreasing AND concave up • both decreasing AND concave down and draw the basic shape of the curve on each interval. Now piece your shapes together to draw the function h ( x ) below. Label all intercepts, local extrema, inﬂection points, removable discontinuities, and asymptotes. 2. Find the absolute maximum and minimum value of the function f ( x ) = 3( x 2-2 x ) 1 3 on the interval [0 , 4] Try to sketch the function on [0 , 4] . Use intercepts and a number line for the ﬁrst derivative, to decide where the function is increasing/decreasing and also the special features at the critical points (vertical tangent, cusp, etc.)....
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P23 - • both decreasing AND concave up • both...

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