Determine the critical points of $f(x)=(x+2)^2$.

First find the derivative. Use the Chain Rule to find that $f\,'(x)=2(x+2)$.

Now set $f\,'(x)=0$ and do some algebra to find the value of $x$. Like so:
$$\begin{eqnarray} f\,'(x)&=&0\\ 2(x+2)&=&0\\ x+2&=&0\\ x&=&-2. \end{eqnarray}$$
The function has only one critical point and it is at $x=-2$.