Lagrange's Mean Value Theorem and Taylor's Theorem and Their Applications

Lagrange's mean value theorem and Taylor's theorem are two important and widely used formulas in calculus courses. In this paper, we introduce the method for proving Lagrange's mean value theorem and Taylor's theorem using Rolle's theorem, and the application of these two theorems in estimating the value of integrals, determining the concavity and convexity of functions, and solving the limits of functions.