Rolle's theorem: Rolle’s theorem is a variation or

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 ... Learn the statement of Rolle's Theorem, its geometrical and algebraic representation and derivation with examples from this page. Explain the meaning of Rolle’s theorem. Describe the significance of the Mean Value Theorem. State three important consequences of the Mean Value Theorem. The Mean Value Theorem is one of the most important theorems in calculus. We look at some of its implications at the end of this section. 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.