The Mean Value Theorem:
If a function f is continuous on the closed interval [a,b] and differentiable on the interval (a,b), then there exists a c in (a,b) such that f'(c)= (f(b)-f(a))/(b-a). In other words there is a c in the interval (a,b) where the slope of the tangent line is equal to the slope of the secant line through (a,f(a)) and (b,f(b)).