Mean Value Theorem/Examples

Examples of Use of Mean Value Theorem

Example: $x^3$: Formulation $1$

Let $f$ be the real function defined as:

$\map f x = x^3$

Let:

$a = 1$, $b = 2$

Then when $\xi = \sqrt {\dfrac 7 3}$:

$\map {f'} \xi = \dfrac {\map f b - \map f a} {b - a}$

Example: $x^3$: Formulation $2$

Let $f$ be the real function defined as:

$\map f x = x^3$

Let:

$c = 2$, $h = -1$

Then when $\theta = 2 - \sqrt {\dfrac 7 3}$:

$\map {f'} {c + \theta h} = \dfrac {\map f {c + h} - \map f c} h$