Write the statements of Rolles’ theorem and Lagrange’s mean value theorem

Rolles’ theorem:

If $f:[a,b]\to R$

Is a function such that

i) $f$ is continuous on $[a, b]$
ii) $f$ is differentiable on $(a, b)$
iii) $f\left(a\right)=f\left(b\right)$
Then there exists atleast one point $c\in (a,b)$ such that $f^{\mathrm{\prime }}\left(c\right)=0$

Lagrange’s mean value theorem :

If $f:[a,b]\to R$ is a function such that

$i)$ $f$ is continuous on $[a, b]$ and
$ii)$ $f$ is differentiable on $(a, b)$

then there exists a point $c\in (a,b)$ such that $f^{\mathrm{\prime }}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$