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

question 37

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

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