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.
Attention reader! Don’t stop learning now. Get hold of all the important CS Theory concepts for SDE interviews with the CS Theory Course at a student-friendly price and become industry ready.
- Mathematics | Rolle's Mean Value Theorem
- Mathematics | Lagrange's Mean Value Theorem
- Bayes's Theorem for Conditional Probability
- Corollaries of Binomial Theorem
- Advanced master theorem for divide and conquer recurrences
- Consensus Theorem in Digital Logic
- Vantieghems Theorem for Primality Test
- Arden's Theorem in Theory of Computation
- Dilworth's Theorem
- Arden's Theorem and Challenging Applications | Set 2
- Kleene's Theorem in TOC | Part-1
- Taylor's Theorem and Taylor series
- Quotient Remainder Theorem
- Mathematics | Mean, Variance and Standard Deviation
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.