The derivative of a function $f$ is given by $f ^ { \prime } ( x ) = ( x - 3 ) e ^ { x }$ for $x > 0$, and $f ( 1 ) = 7$.
(a) The function $f$ has a critical point at $x = 3$. At this point, does $f$ have a relative minimum, a relative maximum, or neither? Justify your answer.
(b) On what intervals, if any, is the graph of $f$ both decreasing and concave up? Explain your reasoning.
(c) Find the value of $f ( 3 )$.