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: $f(b)-f(a)=f'(c)(b-a)$, where c is between b and a.