Mean Value Theorem/Examples/x^3/Formulation 1

Example of Use of Mean Value Theorem
Let $f$ be the real function defined as:
 * $\map f x = x^3$

Let:
 * $a = 1$, $b = 2$

Then when $\xi = \sqrt {\dfrac 7 3}$:
 * $\map {f'} \xi = \dfrac {\map f b - \map f a} {b - a}$

Proof
We have: