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July 10th, 2018, 08:54 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) = tanx10x. 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 12:02 PM. Reason: to add domain 
July 10th, 2018, 10:27 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1474 
Sure looks like infinite roots to me. Did you mean to restrict the domain? 
July 10th, 2018, 10:47 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, 10:53 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1474 
Solve $g'(x)=0$ You'll see there are only 2 solutions on your restricted domain. Now apply Rolle's theorem. 

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