拉格朗日定理

As functions of the function of mathematics, the Key theorem of calculus of variations is Euler LaGrange, it can be used to the pan-seeking function of the maximum and minimum of mathematical.

变分法是处理函数的函数的数学领域，关键定理是欧拉－拉格朗日方程，用来求的泛函数的极大值和极小值的数学方法。

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

A combinatorial identity is obtained:=:~z 2r扟32-rn-iJ As main result of this paper, in section two, the convolution梩ype identities emerge from our discussion about Lagrange formula whom in author 憇 view can be taken as the inherent characteristic of Lagrange formula but have been ignored fOi so long time.

第一章对拉格朗日反演在Riordan群理论中的应用进行了介绍，证明了一个组合等式：第二章通过对拉格朗日反演定理本身的分析，得到一个对任意的形式幂级数都适用的三个拟卷积公式，这些公式体现了任意能在零点解析的函数的内在性质。

Differential intermediate value theorem and the Taylor formula In this paper, leads to Fermat's theorem Rolle Mean Value Theorem, and then constructing auxiliary function of the Lagrange mean value theorem and Cauchy's Mean Value Theorem to prove that.

微分中值定理和泰勒公式本文通过费马定理引出罗尔中值定理，再构造辅助函数对拉格朗日中值定理和柯西中值定理进行证明。

Lagrange value theorem is an important one of the Mean Value Theorem.

拉格朗日中值定理是重要的微分中值定理之一。

This paper gives the new method to prove the Cauchy Mean Value Theorem ,which also may be deduced from the Lagrange Mean Value Theorem.

给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。

This paper describes the content of the theorem, and theorems are given two proofs, cite the Lagrange mean value theorem in the mathematics major applications, including that inequality, identity, Limit, determine monotonicity, root The existence of such.

本文简要叙述了定理的内容，并且给出了定理的两种证明方法，例举了拉格朗日中值定理在数学中的主要应用，包括证明不等式，恒等式，求极限，判断单调性，根的存在性等。

We establish a Lagrange multiplier theorem for strict efficiency in convex settings and express strict points as saddle points of an appropriate Lagrangian function.

讨论凸多目标最优化问题的严有效解，建立了拉格朗日乘子定理，并把严有效解表示为一个适当的拉格朗日函数的鞍

Theorem of mean significance: The application derivative research function's nature wants directly or indirectly with the aid of Yu Zhongzhi,Specially Lagrange theorem of mean,Here is mainly from the equality proof, the inequality proof, existence asks some limits, the determination equation root and so on five aspects to carry on the discussion,so, The theorem of mean is transforms as the function in the sector research important tool, Must bring to the enough attention in the middle of ours study and the teaching.

中值定理意义：应用导数研究函数的性质都要直接或间接地借助于中值，特别是拉格朗日中值定理，这里主要是从等式的证明、不等式的证明、求一些极限、判定方程根的存在性等五个方面来进行讨论，因此，中值定理是转化为函数在区间上的研究的重要工具。在我们的学习与教学当中要引起足够的注意。

On the basis of these theories,Rolle mean value theorem,Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.

在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新