Rolle's theorem: And Lagrange's Mean Value Theorem

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. In calculus, there exists a theorem that guarantees the existence of a point where the slope of the tangent is zero if a function starts and ends at the same value on an interval. This result is known as Rolle’s Theorem. It is one of the core theorems in differential calculus. Rolle's Theorem Graph Formula used for Rolle's Theorem: f' (c) = 0 ... In real analysis, a branch of mathematics, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one point, somewhere between them, at which the slope of the tangent line is zero. Rolle's theorem provides valuable insights into the behavior of differentiable functions and is widely used in calculus, analysis, and various applications in mathematics and science.