Mathematically, the MVT states that if a function f(x) is continuous on the interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in the open interval (a, b) such that the derivative of the function at that point, f'(c), is equal to the average rate of change of the function over the interval, or (f(b) - f(a)) / (b - a).