Lagrange mean value theorem, also known as Laplace theorem, is one of the basic theorems in differential calculus, which reflects the relationship between the overall average rate of change of a differentiable function in a closed interval and the local rate of change of a point in the interval. Lagrange mean value theorem is a generalization of Rolle mean value theorem and a special case of Cauchy mean value theorem. It is a weak form of Taylor formula (first-order expansion).
History:
1797, the French mathematician Lagrange put forward this theorem in the sixth chapter of his book Analytic Function Theory, and made a preliminary proof, so people named it Lagrange Mean Value Theorem. ?