Find the Critical Points of the Function $f ( x , y , z ) = - 3 - ( ( x + 8 ) ( y - 7 ) ( z - 3 ) ) ^ { 2 }$

Multiple Choice

Find the critical points of the function $f ( x , y , z ) = - 3 - ( ( x + 8 ) ( y - 7 ) ( z - 3 ) ) ^ { 2 }$ , and, from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

A) relative minima at $( - 8 , a , b )$ , $( c , 7 , d )$ , $( m , n , 3 )$ , where $a , b , c , d , m,$ and $n$ are arbitrary real numbers
B) relative maxima at $( - 8 , a , b )$ , $( c , 7 , d )$ , $( m , n , 3 )$ , where $a , b , c , d , m,$ and $n$ are arbitrary real numbers
C) relative minimum at $( - 8,7,3 )$
D) relative maximum at $( - 8,7,3 )$
E) no relative extrema