# Rolle's theorem

Rolle's theoremnoun

A theorem stating that if a curve is continuous, has two

*x*-intercepts, and has a tangent at every point between the intercepts, at least one of these tangents is parallel to the*x*-axis.Origin of Rolle's theorem

*After Michel*

*Rolle*

*(1652-1719), French mathematician*

## rolle-s-theorem

Noun

(*plural not attested*)

- (calculus) A theorem stating that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero.