[kō·shē ¦mēn ¦val·yü ‚thir·əm] (mathematics) The theorem that if ƒ and g are functions satisfying certain conditions on an interval [a,b ], then there is a point x in the interval at which the ratio of derivatives ƒ′(x)/ g ′(x) equals the ratio of the net change in ƒ, ƒ(b) - ƒ(a), to that of g.