Cauchy's Mean-Value Theorem

Cauchy's mean-value theorem is a generalization of the usual mean-value theorem. It states that if  and  are continuous on the closed interval , if , and if both functions are differentiable on the open interval , then there exists at least one  with  such that

(Hille 1964, p. 340).

REFERENCES:

Hille, E. Analysis, Vol. 1. New York: Blaisdell, 1964.