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

Question

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

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The Answer of 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

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

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