KnowraRolle's theoremLinked fromLinked fromThe 9 pages that link to Rolle's theorem, each with the reason it gives.All 9Broader topic 1Related 4Compared with 4Mean value theoremBroader topic: It is the zero-average-change special case that underlies the mean value theorem.Darboux's theoremRelated: It supplies the critical-point argument behind the intermediate-value behavior of derivatives.Cauchy's mean value theoremRelated: Applying it to a tailored difference of the two functions yields the theorem’s point.Gauss–Lucas theoremCompared with: It is the real-variable counterpart to the derivative-root location phenomenon.Bolzano's theoremCompared with: It also guarantees an interior point, but through endpoint equality and differentiability.Casas-Alvero conjectureCompared with: It links roots of a real function to derivative roots, unlike the conjecture's shared-root requirement.Four-vertex theoremRelated: Repeated applications turn periodicity and symmetry constraints into extrema.Interior extremum theoremRelated: The interior-extremum condition is the key fact behind its standard proof.Marden's theoremCompared with: It is the real-variable ancestor of interlacing intuitions, but does not specify an ellipse.