Rolle’s theorem is a special case of the Mean Value Theorem. In Rolle’s theorem, we consider differentiable functions f defined on a closed interval [a,b] with f(a)=f(b). The Mean Value Theorem generalizes Rolle’s theorem by considering functions that do not necessarily have equal value at the endpoints. Consequently, we can view the Mean Value Theorem as a slanted version of Rolle’s theorem (Figure 0.00). The Mean Value Theorem states that if f is continuous over the closed interval [a,b] and differentiable over the open interval (a,b), then there exists a point c∈(a,b) such that the tangent line to the graph of f at c is parallel to the secant line connecting (a,f(a)) and (b,f(b)).