PickThe mid-value theorems is a series of mean value theorems in general, is a powerful tool research function. It includes luol theorem, Lagrange theorem and cauchy theorem, Taylor theorem. The mid-value theorems is the core of differential calculus theorem, the important tool of function, attention. Over the past few decades, people in real field on differential mid-value theorem on a lot of research. This paper mainly introduces several different methods to prove the mid-value theorem, at the same time the mid-value theorem is applied in the mathematical theory, such as the application and mathematical : value theorem, proof, application, mathematical modeling
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