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-   -   How many solutions to the following equation (http://mymathforum.com/calculus/344541-how-many-solutions-following-equation.html)

Mathmatizer July 10th, 2018 07:54 AM

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

romsek July 10th, 2018 09:27 AM

Sure looks like infinite roots to me.

Did you mean to restrict the domain?

Mathmatizer July 10th, 2018 09:47 AM

My bad :o. 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!)

romsek July 10th, 2018 09:53 AM

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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