MTH132-Quiz4 - 1 2(find c such that c f a b a f b f = and...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: March 16, 2009 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) 3 ' x y = (b) 2 1 1 ' x y - = (c) 2 cos ' x y = (d) 2 ) ( ' - = x x f and the graph of ) ( x f passes through the point ) 0 , 2 ( . 2. Suppose 5 6 ) ( 3 + + = x x x f (a) [2 pts]. Use Intermediate Value Theorem to show that 0 ) ( = x f has a root in the interval ] 1 , 1 [ - .
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Page 2 10/18/2011 (b) [2 pts]. Verify the Mean Value Theorem on the interval
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Unformatted text preview: ] 1 , 2 [--. (find c such that ) ( ' ) ( ) ( c f a b a f b f =--, and show that c belongs to this interval) 3. Let 2 3 ) ( 2 3 + +-= x x x g , domain is ) , ( ∞-∞ . (a) [1 pts]. Find the derivative of ) ( x g . (b) [1 pts]. Find all the critical points. (c) [2 pts]. Use critical points to divide the domain into subintervals. Find where the curve is increasing and where it is decreasing. (d) [bonus 2 pts]. Identify the local extrema and global extrema, if any....
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MTH132-Quiz4 - 1 2(find c such that c f a b a f b f = and...

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