Mean Value Theorem

If f(x) is continuous on [a, b] and differentiable on (a, b), then there exists a point c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Geometrically, the Mean Value Theorem implies that if we plot the graph of a function on a coordinate plane, there must be at least one tangent line that is parallel to the secant line connecting the endpoints of the interval [a, b].