220FinalExamC

220FinalExamC - MATH 220, SPRING 2009 FINAL EXAMINATION...

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MATH 220, SPRING 2009 FINAL EXAMINATION (VERSION C) (i) Write your name, your TA’s name and your discussion section number (or time) on each answer sheet. (ii) Start your answer to each question on a new answer sheet and continue on the back if you need more space. (iii) No books, notes, calculators or other electronic devices are allowed. (iv) For full credit, show clearly all your work. 1. (16 points) For each of the following functions f ( x ) , find its derivative f 0 ( x ) : ( i ) f ( x ) = ln x 1 + e x ( ii ) f ( x ) = (1 + 2 x ) 3 e x . ( iii ) f ( x ) = ln( x + x 2 ) ( iv ) f ( x ) = e (1+1 /x ) 2. (12 points) (i) Find the equation of the tangent line to the graph of the function f ( x ) = x 3 + 2 x + 2 at the point on the graph at which x = 0 . (ii) Find the coordinates of the point(s) on the graph of the function f ( x ) = x 3 + 2 x at which the tangent line parallel to the line y = 5 x + 1? 3. (12 points) A furniture store expects to see 640 sofas at a steady rate over the year.
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220FinalExamC - MATH 220, SPRING 2009 FINAL EXAMINATION...

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