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

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

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