拉格朗日中值定理證明及其應用

李兵方

摘要：拉格朗日中值定理是微分學突出的成果，在微積分中占有非常重要的地位，且它是微分學的基礎定理之一，是溝通函數與導數之間的橋梁，在理論及其應用上都有極其重要的意義。通過對定理的再認識，對拉格朗日中值定理的應用做了一定研究，主要探討了拉格朗日中值定理在求極限、證明不等式、證明函數單調性等方面的應用。

關鍵詞：拉格朗日定理;羅爾定理;應用

中圖分類號：O171 ? ? 文獻標志碼：A ? ? 文章編號：1674-9324（2020）14-0294-02

Abstract：Lagrange theorem is differential prominent achievements in the mathematical analysis plays a very important position，and it is the basis of theorem of differential calculus is one of communication between function and derivative of the bridge，in the theory and its applications all have very important meaning.Recognition by theorem of Lagrange's theorem to do an analysis，on the application of Lagrange theorem to do a little research，a comprehensive understanding of the Lagrange mean value theorem in limit，to prove inequality，that function monotonicity aspects of role to play on the theorem in-depth understanding and mastery of the role can be applied correctly.

Key words：Lagrange;Rolle theorem;application