Find the Critical Points of the Function $f ( x , y , z ) = ( x - 4 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z - 2 ) ^ { 2 }$

question 66

Multiple Choice

Find the critical points of the function $f ( x , y , z ) = ( x - 4 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z - 2 ) ^ { 2 }$ , and, from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

• A)relative minimum at \(( - 4 , - 7 , - 2 )\)
• B)relative maximum at \(( - 4 , - 7 , - 2 )\)
• C)relative minimum at \(( 4,7,2 )\)
• D)relative maximum at \(( 4,7,2 )\)
• E)no relative extrema

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