Rolle's theorem

In calculus, Rolle's theorem states that, given two equal endpoints on the curve of a differentiable function, there exists at least one point between the endpoints where the tangent line is perfectly horizontal.[cite:@openstax2020calculus] The theorem is a special case of the mean value theorem but was proved about a century prior and without the tools of modern calculus.[cite:@enwiki:1307164365]

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