220FinalExamB

# 220FinalExamB - MATH 220 SPRING 2009 FINAL...

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MATH 220, SPRING 2009 FINAL EXAMINATION (VERSION B) (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 + x ( ii ) f ( x ) = x 3 e x . ( iii ) f ( x ) = ln( x + x ) ( 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 5 + 2 at the point on the graph at which x = 1 . (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 has slope equal to 5 . 3. (12 points) A closed rectangular box is to be constructed. The base of the box is square. The box must have a volume of 12 cu.ft. The material for the bottom costs \$2 per

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220FinalExamB - MATH 220 SPRING 2009 FINAL...

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