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 July 10th, 2018, 07:54 AM #1 Newbie   Joined: Oct 2017 From: Here Posts: 19 Thanks: 0 How many solutions to the following equation How to prove that tanx=10x has exactly 3 roots in the interval (-pi/2, pi/2)? I defined g(x) = tanx-10x. I think I should derive it and use Rolle's theorem and Intermediate value theorem. But I just can't figure out how exactly. Thanks Last edited by skipjack; July 10th, 2018 at 11:02 AM. Reason: to add domain
 July 10th, 2018, 09:27 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,405 Thanks: 1306 Sure looks like infinite roots to me. Did you mean to restrict the domain? Thanks from Mathmatizer
 July 10th, 2018, 09:47 AM #3 Newbie   Joined: Oct 2017 From: Here Posts: 19 Thanks: 0 My bad . the domain is restricted to (-pi/2, pi/2) (cannot edit the main post anymore, if a moderator can add the domain to the main post it would be great!)
 July 10th, 2018, 09:53 AM #4 Senior Member     Joined: Sep 2015 From: USA Posts: 2,405 Thanks: 1306 Solve $g'(x)=0$ You'll see there are only 2 solutions on your restricted domain. Now apply Rolle's theorem. Thanks from Mathmatizer

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