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Definition of ROLLE'S THEOREM
: a theorem in mathematics: if a curve is continuous, crosses the x-axis at two points, and has a tangent at every point between the two intercepts, its tangent is parallel to the x-axis at some point between the intercepts
Origin of ROLLE'S THEOREM
Michel Rolle †1719 French mathematician
First Known Use: circa 1891
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.