The application of variation of parameters to the construction of auxiliary functions in the proof of differential mean value theorem
ZHU Cunbin
Abstract：To prove some median problems by using differential mean value theorem to construct auxiliary functions,the key step is to construct appropriate auxiliary functions and to verify the conditions of relevant theorems for auxiliary functions,the auxiliary function obtains the conclusion of the theorem,thus the identical deformation obtains the conclusion which needs to prove.In this paper,we give a general method of constructing auxiliary functions——variation of parameters for the proof of differential mean value theorem.In this paper,we give the variation of parameters thought and the specific derivation process,and the derivation process through the first-order,second-order and third-order concrete problems.Finally,we give the conclusion of constructing auxiliary functions for general problems.
Keywords：variation of parametersauxiliary functionsRolle's theoremlinear homogeneous differential equation
Publication Date：2023-09-15
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 243-249 )