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July 10th, 2018, 07:54 AM   #1
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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.

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Last edited by skipjack; July 10th, 2018 at 11:02 AM. Reason: to add domain
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July 10th, 2018, 09:27 AM   #2
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Sure looks like infinite roots to me.

Did you mean to restrict the domain?
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July 10th, 2018, 09:47 AM   #3
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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!)
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July 10th, 2018, 09:53 AM   #4
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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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