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How many solutions to the following equationHow 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 |

Sure looks like infinite roots to me. Did you mean to restrict the domain? |

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!) |

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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