The extension and application of differential mean value theorem
By using the idea of substitution and constructing appropriate auxiliary functions,the Rolle's mean value theorem,Lagrange's mean value theorem,and Cauchy's mean value theorem were comprehensively extended.The application of these extended mean value theorems in proving differential equations and inequalities was explained through examples.
Rolle's mean value theoremLagrange's mean value theoremCauchy's mean value theoremauxiliary functiondifferential inequality
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