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 June 12th, 2015, 03:15 AM #1 Newbie   Joined: Jun 2015 From: England Posts: 1 Thanks: 0 Intermediate Value Theorem Problem I know this problem is to do with the IVT but I'm not sure where to start- could somebody please give me a hint- thanks Suppose that F: R---> R is continuous at every point. Prove that the equation F(x) = c cannot have exactly two solutions for every value of c. June 12th, 2015, 06:54 PM #2 Global Moderator   Joined: May 2007 Posts: 6,852 Thanks: 743 General idea. Pick a pair of points x1 and x2 (> x1), where f(x1)=f(x2). All x's, where x1 f(x1) or all < f(x1). Otherwise intermediate value theorem gives a third point x0 in the interval where f(x0)=f(x1). Now the problem is reduced to showing that f(x) (assume > f(x1)) has a max, which is unique. Tags intermediate, problem, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jiasyuen Calculus 3 January 5th, 2015 06:11 AM nubshat Calculus 1 October 23rd, 2013 01:32 AM hooperoo Real Analysis 2 April 16th, 2013 01:40 AM chris123 Real Analysis 0 February 21st, 2013 06:44 PM Twoxsmart Calculus 1 January 28th, 2009 10:55 PM

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