Definition of mean-value theorem in English:

mean-value theorem


  • An elementary theorem in mathematical analysis, which states that if a real function f(x) is continuous on the closed interval a ≦ x ≦ b and differentiable on the open interval a < x < b, then there is a point in the open interval at which the first derivative of the function is equal to f(b) − f(a)/b − a.


Early 20th century; earliest use found in Transactions of the American Mathematical Society.