# Where is Rolle's Theorem true?

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f(x) = 2 tan(x/2) find the point in the interval [0, 2pi] where the conclusion of Rolle's Theorem is true

f(x) = 2 tan(x/2) find the point in the interval [0, 2pi] where the conclusion of Rolle's Theorem is true

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Given

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Rolle's Theorem is true for any continuous function ( f(x) ) that is differentiable on the closed interval ([a, b]), where ( f(a) = f(b) ). In other words, if a function is continuous on a closed interval and differentiable on the open interval, and it takes the same values at the endpoints of the interval, then there exists at least one point ( c ) in the open interval ((a, b)) such that the derivative of the function evaluated at ( c ) is equal to zero.

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