- It has been proposed that this page, :Mean value theorem, be titled, "Mean value theorem".
The Mean Value Theorem of Calculus states that for some value c on the function f on some interval [a, b], f'(c) (the slope of f at c) will equal the average slope over [a, b], provided that f is continuous over the interval [a, b] and differentiable on the interval (a, b).
This is written algebraically as: 
, where c is between b and a.