The Mean Value Theorem
Let f be a function that satisfies the following hypotheses:
• f is continuous on the closed interval [a,b]
• f is differentiable on the open interval (a,b)
Then there is a number c in (a,b) such that f'(c)=f(b)-f(a)/b-a
or equivalently f (b) = f (a) f '(c)(b − a)