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

question 34

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

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Definitions:

Hammer

A tool consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object.

Anvil

A heavy iron block used in metalworking as a surface upon which metals can be hammered and shaped.

Auditory Cortex

The part of the brain that processes auditory information, located in the temporal lobe.

Temporal Lobe

A region of the cerebral cortex responsible for processing auditory information and is involved in memory and emotion.