Lagrange's Mean Value Theorem
Revision as of 10:22, 15 February 2008 by Shreyas patankar (talk | contribs) (New page: '''Lagrange's mean value theorem''' or LMVT is considered one of the most important results in real analysis. An elegant proof of the Fundamental Theorem of Calculus can be given using...)
Lagrange's mean value theorem or LMVT is considered one of the most important results in real analysis. An elegant proof of the Fundamental Theorem of Calculus can be given using LMVT.
Statement
Let
Let be continous on
and differentiable on
.
Then
such that
Proof
We reduce the problem to the Rolle's theorem by using an 'auxillary function'.
Consider
note that
By Rolle's theorem, such that
i.e.
or
QED