# Rolle's theorem

Rolle's theorem may be stated as follows. Suppose a continuous function (see continuity)
crosses the *x*-axis at two points *a* and *b* and
is differentiable at all points between *a* and *b*; that
is it has a tangent at all points on the
curve between *a* and *b*. Then there is at least one point
between *a* and *b* where the derivative is 0, and the tangent is parallel to the *x*-axis.