Cauchy Mean Value Theorem

A generalization of the mean value theorem: if f and g are continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that (f(b)-f(a)) g'(c) = (g(b)-g(a)) f'(c); equivalently, there exists c where the ratio of increments equals the ratio of derivatives if g'(c)≠0.