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Special case of the mean-value theorem of differential calculus. It states that if a continuous curve passes through the x-axis twice within a given interval and has a unique tangent line at every point of that interval, then somewhere between the two points of interception it has a tangent parallel to the x-axis.
This entry comes from Encyclopædia Britannica Concise. For the full entry on Rolle's theorem, visit Britannica.com.