Maxima and Minima in Discontinuous Functions

For the question, choose the correct answers from the given options:
Statement I: For the function $f\left(x\right)=\left\{\begin{array}{ll}15-x,& x<2\\ 2x-3,& x\ge 2\end{array}\right.$, $x=2$ has neither a maximum nor a minimum point.
Statement II: $f^{\text{'}}\left(x\right)$ does not exist at $x=2$.