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Unformatted text preview: Project 20/21 MAC 2233 1. Note that the information learned in this lecture should prepare you for curve sketching!! Recall this function from a prior project: f ( x ) = 3 x ( 7- x 2 ) 2 3 f ( x ) = 7(3- x 2 ) ( 7- x 2 ) 1 3 f 00 ( x ) =- 28 x ( 9- x 2 ) 3( 7- x 2 ) 4 3 (Again, if you want extra practice with differentiation/factoring, verify these on your own.) On what intervals is f ( x ) increasing? decreasing? (Include a number line.) inc (- ,- 7 ) , (- 3 , 3 ) , ( 7 , ) dec (- 7 ,- 3 ) , ( 3 , 7 ) 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. local max: x =- 7 (cusp); x = 3 (HTL) local min: x =- 3 (HTL); x = 7 (cusp) On what intervals is f ( x ) concave up? concave down? (Include a number line.) What are the inflection points for f ( x ) ?...
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- Spring '08