Rolle’s theorem cannot be applicable for 

$f\left(x\right)=3+(x-1{)}^{2/3}\Rightarrow f^{\mathrm{\prime }}(x)=\frac{2}{3}(x-1{)}^{-1/3}$

is not defined at $x = 1$

Rolle’s theorem cannot be applicable for

$f\left(x\right)=3+(x-1{)}^{2/3}\text{ in }[0,3]$