MTH132-Quiz4-Solutions (1)

# MTH132-Quiz4-Solutions (1) - Page 1 10/18/2011 Name (Print...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: Oct 20, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 15 minutes. 1 [3 pts each] . Find all possible functions with the given derivatives. (a) 2 ' x y = C x y + = 3 3 1 (b) 2 1 ' x y - = C x C x y + = + - + - = - - 1 1 ) 2 ( 1 1 (c) x y 2 sin ' = C x y + - = 2 cos 2 1 (d) 1 2 ) ( ' - = x x f and the graph of ) ( x f passes through the point ) 0 , 0 ( . C x x x f + - = 2 ) ( and 0 0 0 0 ) 0 ( = = + - = C C f So x x x f - = 2 ) ( 2. Suppose 1 3 ) ( 4 + + = x x x f (a) [2 pts]. Use Intermediate Value Theorem to show that 0 ) ( = x f has a root in the interval ] 1 , 2 [ - - . 1. 1 3 ) ( 4 + + = x x x f is continuous on R. 2. 1 ) 1 ( , 11 ) 2 ( - = - = - f f So ) 1 ( 0 ) 2 ( - - f f and by Intermediate Value Theorem , there is a root in the interval ] 1 , 2 [ - -

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Page 2 10/18/2011 (b) [2 pts]. Show that
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## This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Quiz4-Solutions (1) - Page 1 10/18/2011 Name (Print...

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