October 1st, 2013, 12:39 PM  #1 
Newbie Joined: Oct 2013 Posts: 5 Thanks: 0  Applying Rolle's Theorem
Prove that if a function is continuous on a segment [a,b] and , then there exists a point such that . Hint: Apply Rolle's Theorem to the function where . 
October 1st, 2013, 01:49 PM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115  Re: Applying Rolle's Theorem
g(a) = g(b) = 0, hence by Rolle's theorem, there exists c, such that g'(c) = 0. Hence: 

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