Step 1 :Given that $f(x)$ has a local max at $x=7$ and neither a local max nor a local min at $x=2$.
Step 2 :From the first derivative test, we know that if $f(x)$ has a local max at $x=a$, then $f^{\prime}(a)=0$.
Step 3 :From the second derivative test, we know that if $f(x)$ has a local max at $x=a$, then $f^{\prime \prime}(a)<0$.
Step 4 :So, the statement $f^{\prime}(7)=0$ and $f^{\prime \prime}(7)=-5$ is consistent with the given information.
Step 5 :Since $f(x)$ has neither a local max nor a local min at $x=2$, $f^{\prime}(2)$ can be any real number except 0.
Step 6 :Also, $f^{\prime \prime}(2)$ can be any real number.
Step 7 :So, the statement $f^{\prime}(2)=3$ and $f^{\prime \prime}(2)=0$ is consistent with the given information.
Step 8 :Final Answer: The statements that are consistent with the given information are \(\boxed{A}\) and \(\boxed{B}\).