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Cauchy's Mean Value Theorem
Definition: Cauchy's mean-value theorem is a generalization of the usual mean-value theorem. It states that if f(x) and g(x) are continuous on the closed interval [a,b], if g(a) does not equal g(b), and if both functions are differentiable on the open interval (a,b), then there exists at least one c with a<c<b such that (f(b)-f(a)) / (g(b)-g(a)) = (f '(c)) / (g '(c)).