Cauchy’s Mean Value Theorem



Suppose f(x) and g(x) are 2 functions satisfying three conditions:

1) f(x), g(x) are continuous in the closed interval a <= x <= b

2) f(x), g(x) are differentiable in the open interval a < x < b and

3) g'(x) != 0 for all x belongs to the open interval a < x < b

Then according to Cauchy’s Mean Value Theorem there exists a point c in the open interval a < c < b such that:

[f(b) - f(a)] / [g(b) - g(a)] = f'(c) / g'(c)

The conditions (1) and (2) are exactly same as the first two conditions of Lagranges Mean Value Theorem for the functions individually. Lagranges mean value theorem is defined for one function but this is defined for two functions.



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.


Article Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.