On the Cauchy Differential Mean Value Theorem Proof Train of Thought

In order to cultivate the students’ mathematical thinking, and improve the innovative ability of students, an exploration is made into the proof methods for the Cauchy differential mean value theorem from multiple perspectives via all-round approaches. Summed up are the proof methods for the Cauchy differential mean value theorem by aid of the Rolle’s theorem, increment, monotonicity, Cauchy determinant, definite integral and complex function. Using the analytical method, the train of thought by constructing certain auxiliary functions is also subjected to a detailed examination.