The Mean Value Theorem
If f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that f'(c) = [f(b)-f(a)]/(b-a).
What It Means
At some point, the instantaneous rate of change equals the average rate of change over the interval.
Applications
The MVT is used in physics, economics, and to prove other calculus theorems.