Chapter 9 - Section 9.9 - Convergence of Taylor Series - Exercises - Page 542: 45

It has been verified that the Mean Value Theorem is a special case of Taylor’s Theorem.

Consider the special case for Taylor’s Theorem as follows: $ f(b) =f(a)+f’(c)(b-a)$ Here, $ c $ is between $ a $ and $ b $, so $ f(b) =f(a)+f’(c) (b-a)$ and $ f(b) -f(a)=f’(c) (b-a)$ Hence, the result has been verified that the Mean Value Theorem is a special case of Taylor’s Theorem.