Based on the Rolle mid-value theorem, by using determinant method, the Lagrange mid-value theorem and Cauchy mid-value theorem are obtained, and some new results are discovered.

• 本文从罗尔中值定理出发，这用行列式理论，不仅证明了拉格朗日中值定理和柯西中值定理，还发现了一些新的结论。