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Abstract: Lagrange (Lagrange) value theorem is an important one of the Mean Value Theorem. This paper describes the content of the theorem, and theorems are given two proofs, cite the Lagrange mean value theorem in the mathematics major applications, including that inequality, identity, Limit, determine monotonicity, root The existence of such. Lagrange mean value theorem on the wrong usage of some brief analysis. Finally, Theorem weakened condition, to promote more general form.
Keywords: Lagrange mean value theorem; limit; inequality; root existence; Promotion