If $\underset{x\to a}{\mathrm{l}\mathrm{i}\mathrm{m}}f\left(x\right)=\underset{x\to a}{\mathrm{l}\mathrm{i}\mathrm{m}}\left[f\left(x\right)\right]$ ($\left[·\right]$ denotes the greatest integer function) and $f\left(x\right)$ is non-constant continuous function, then

Consider the graph of the function $f\left(x\right)=x+\sqrt{\left|x\right|}$

Statement $1:$ The graph of $y=f\left(x\right)$ has only one critical point.

Statement $2:$ $f^{\text{'}}\left(x\right)$ vanishes only at one point.