2007Unpublished venueRequires access

A Note on the Differential Mean-value Theorem

Song Xiu-ying

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Abstract

The text think G.darboux theorem from a new angle,use the continuous function lying between value theorem and Lagrange value theorem mainly,through two pieces of function of assisting F(x) and φ(x) with setting up the connection between above-mentioned two theorem,discuss respectively under various kinds of situations,the conclusion of the theorem must happen finally.

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What this paper is about

The text think G.darboux theorem from a new angle,use the continuous function lying between value theorem and Lagrange value theorem mainly,through two pieces of function of assisting F(x) and φ(x) with setting up the connection between above-mentioned two theorem,discuss respectively under various kinds of situations,the conclusion of the theorem must happen finally.

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Available abstract

The text think G.darboux theorem from a new angle,use the continuous function lying between value theorem and Lagrange value theorem mainly,through two pieces of function of assisting F(x) and φ(x) with setting up the connection between above-mentioned two theorem,discuss respectively under various kinds of situations,the conclusion of the theorem must happen finally.

Key concepts: Mean value theorem (divided differences), Mathematics, Fundamental theorem of calculus, Danskin's theorem, Picard–Lindelöf theorem, Brouwer fixed-point theorem, Connection (principal bundle), Value (mathematics)

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