Find the Critical Points of the Function $f ( x , y , z ) = ( x - 4 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z - 2 ) ^ { 2 }$

Multiple Choice

Find the critical points of the function $f ( x , y , z ) = ( x - 4 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z - 2 ) ^ { 2 }$ , and, from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

A) relative minimum at $( - 4 , - 7 , - 2 )$
B) relative maximum at $( - 4 , - 7 , - 2 )$
C) relative minimum at $( 4,7,2 )$
D) relative maximum at $( 4,7,2 )$
E) no relative extrema