In calculus, Rolle's theorem states that if a differentiable function (real-valued) attains equal values at two distinct points then it must have at least one fixed point somewhere between them where the first derivative is zero. Rolle's theorem is named after Michel Rolle, a French mathematician. Rolle's Theorem and Lagrange's Mean Value Theorem: Mean Value Theorems (MVT) are the basic theorems used in mathematics. They are used to solve various types of problems in Mathematics. Rolle’s theorem is a variation or a case of Lagrange’s mean value theorem. The mean value theorem follows two conditions, while Rolle’s theorem follows three conditions. This topic will help you understand Rolle’s theorem, its geometrical interpretation, and how it is different from the mean value theorem. We will also study numerical examples related to Rolle’s theorem. What Is Rolle’s Theorem? Rolle’s Theorem is a theorem stating that if a continuous function attains two ... Rolle’s theorem states that if a function is continuous and differentiable on an interval, and has the same value at the endpoints, then there is a point where the derivative is zero. Learn the formula, proof, and how to apply it with graphs and examples.
