Plenty. For example $f(x)=x$ has no critical points. Neither does $f(x)=e^x$.
And your function has no critical points, according to many definitions. Some definitions would include endpoints among the critical points. In that case, if we consider the function as having domain $[4,7]$, you have $4$ and $7$.
The function is continuous on the interval $[4,7]$. So it does attain a maximum and a minimum in the interval. Since the derivative is defined everywhere in the interval, and nowhere $0$, the endpoints $4$ and $7$ are your only candidates for maximumhood/minimumhood.