# P18 - Project 18 MAC 2311 1 Note that the information...

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Project 18 MAC 2311 1. Note that the information learned in this lecture should prepare you for curve sketching. .. Here’s a function you probably can’t visualize: f ( x ) = 3 x ( 7 - x 2 ) 2 3 f 0 ( x ) = 7(3 - x 2 ) ( 7 - x 2 ) 1 3 f 00 ( x ) = - 28 x ( 9 - x 2 ) 3( 7 - x 2 ) 4 3 On what intervals is f ( x ) increasing? decreasing? (Include a number line.) What are the critical numbers for f ( x ) ? Determine whether any are local extrema using the ﬁrst derivative test. For each one that you ﬁnd, label it as a cusp or a horizontal tangent and draw its shape. On what intervals is f ( x ) concave up? concave down? (Include a number line.) What are the inﬂection points for f ( x ) ? On what intervals is the function f ( x ) : both increasing AND concave up both increasing AND concave down both decreasing AND concave up both decreasing AND concave down Next to each interval above, draw the basic shape of the curve on the interval. ( There are four possibilities: each would be the left or right half of the shapes

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## This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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P18 - Project 18 MAC 2311 1 Note that the information...

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