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

question 45

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

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