Mean Value Theorem/Examples/x^3/Formulation 2

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

Let:
 * $c = 2$, $h = -1$

Then when $\theta = 2 - \sqrt {\dfrac 7 3}$:
 * $\map {f'} {c + \theta h} = \dfrac {\map f {c + h} - \map f c} h$

Proof
We have:

and we see that:


 * $1 < 2 - \sqrt {\dfrac 7 3} < 2$