Mean Value Theorem: Introduction

Mean Value Theorem: Introduction

The Mean Value Theorem (MVT) says if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b) then there is at least one value x=c such that f'(c ) equals the average slope between (a,f(a)) and (b,f(b)). Notice the MVT is very similar to Rolle’s Theorem, except it does not have the restriction that f(a) must equal f(b).