Find the Critical Points of the Function $f ( x , y , z ) = 8 - ( ( x - 7 ) ( y + 5 ) ( z - 6 ) ) ^ { 2 } , \text { and }$

Multiple Choice

Find the critical points of the function $f ( x , y , z ) = 8 - ( ( x - 7 ) ( y + 5 ) ( z - 6 ) ) ^ { 2 } , \text { and }$ from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

A) relative maxima at $( 7 , a , b ) , ( c , - 5 , d ) , ( m , n , 6 )$ , where $a , b , c , d , m$ , and $n$ are arbitrary real numbers
B) relative minima at $( 7 , a , b ) , ( c , - 5 , d ) , ( m , n , 6 )$ , where $a , b , c , d , m$ , and $n$ are arbitrary real numbers
C) relative minimum at $( 7 , - 5,6 )$
D) relative maximum at $( 7 , - 5,6 )$
E) no relative extrema