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231sampleexam3solution

# 231sampleexam3solution - MA 23100 NAME PUID Exam 3...

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MA 23100 NAME: Exam 3 PUID: INSTRUCTIONS No books or notes are allowed. You may use a one-line scientific calculator. No other electronic device is allowed. Be sure to turn off your cellphone. Show all your work in the space provided. Little or no credit may be given for an answer with insufficient or inconsistent work, even if the answer happens to be correct. Write answers in the boxes provided. All answers are expected to be simplified ( 2 4 1 2 , 2 x + x 3 x , e ln 2 2, etc). Question Possible Score 1 30 2 10 3 12 4 12 5 12 6 12 7 12 Total 100 1

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1.) (30 pts) Find f 0 ( x ) for each of the following functions: (a) f ( x ) = e 3 x 2 f 0 ( x ) = 6 xe 3 x 2 (b) f ( x ) = ln x x 5 f 0 ( x ) = 1 - 5 ln x x 6 (c) f ( x ) = ln( e 2 x + 1) f 0 ( x ) = 2 e 2 x e 2 x +1 (d) f ( x ) = ln x 4 5 x +7 f 0 ( x ) = 15 x 4 +28 x 3 x 4 (5 x +7) (e) f ( x ) = x 3 e - 4 x f 0 ( x ) = (3 x 2 - 4 x 3 ) e - 4 x 2
2.) (10 pts) Let f ( x ) = x 3 - 3 x 2 - 9 x + 1 . Find the absolute maximum and absolute minimum values of f ( x ) over the interval [ - 2 , 2]. f 0 ( x ) = 3 x 2 - 6 x - 9 = 3( x - 3)( x + 1) f 0 ( x ) = 0 at x = 3 and x = - 1. x = 3 is outside the interval [ - 2 , 2], so we don’t consider it, but we do have to consider the endpoints of the interval.

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231sampleexam3solution - MA 23100 NAME PUID Exam 3...

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