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c1-t4t-a - NAME: Brief Answers TEST-4T/MAC2311 Page 1 of 5...

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NAME: Brief Answers TEST-4T/MAC2311 Page 1 of 5 Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Be careful. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Do not "box" your answers. Communicate. Show me all the magic on the page. 1. (16 pts.) Fill in the blanks of the following analysis with the correct terminology. Let f(x) = x 4 -8 x 3 . Then f ( x )=4 x 3 - 24x 2 =4 ( x-0 ) 2 (x - 6). Consequently,x=0a n dx=6a r e critical (stationary) points of f. Since f ( x )>0f o r6<x , fi s increasing on the set (6, ). Also, because f ( x )<0 w h e n0<x<6 o rx<0 , and f is continuous, f is decreasing on the interval (- , 6). Using the first derivative test, it follows that f has a(n) relative minimum a tx=6 ,a n d neither a relative max nor a relative min a tx=0 . Since f (x) = 12x 2 - 48x = 12x (x - 4), we have f ( 0 )=0 , f ( 4 )=0 ,f ( x )<0w h e n0<x<4 ,a n
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This note was uploaded on 12/26/2011 for the course MAC 2311 taught by Professor Staff during the Fall '08 term at FIU.

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c1-t4t-a - NAME: Brief Answers TEST-4T/MAC2311 Page 1 of 5...

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