Rolle's theorem

(redirected from Rolle theorem)
Also found in: Encyclopedia.
Related to Rolle theorem: Mean value theorem

Rolle's theorem

 (rôlz, rōlz)
n.
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.

[After Michel Rolle (1652-1719), French mathematician.]
References in periodicals archive ?
Then by the Rolle theorem, there exists [xi] [member of] (-L,L) such that [F.sup.(4)]([xi]) = 0.
The points -L, L, [x.sub.a] and [x.sub.b] are zeros of the function W(x) := c(x) - [c.sub.p](x), so by the Rolle theorem there exists [[gamma].sub.i] [member of] (-L,L) such that W'([[gamma].sub.i]) = 0, i = [bar.1, 3].