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:
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.
- Dilworth's Theorem
- Corollaries of Binomial Theorem
- TOC | Kleene's Theorem Part-1
- Mathematics | Rolle's Mean Value Theorem
- Mathematics | Lagrange's Mean Value Theorem
- Vantieghems Theorem for Primality Test
- Arden's Theorem and Challenging Applications | Set 2
- Theory of Computation | Arden's Theorem
- Digital Logic | Consensus theorem
- Bayes's Theorem for Conditional Probability
- Advanced master theorem for divide and conquer recurrences
- Benefits of writing GATE exam
- Compiler Design | Recursive Descent Parser
- Computer Network | Efficiency of Stop & Wait
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.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.