Find the Critical Points of the Function $f ( x , y , z ) = ( x + 7 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z + 6 ) ^ { 2 }$

Multiple Choice

Find the critical points of the function $f ( x , y , z ) = ( x + 7 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z + 6 ) ^ { 2 }$ and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

A) relative minimum at $( 7 , - 7,6 )$
B) relative maximum at $( - 7,7 , - 6 )$
C) relative maximum at $( 7 , - 7,6 )$
D) relative minimum at $( - 7,7 , - 6 )$
E) no relative extrema