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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Definitions:

Operant Conditioning

A method of learning that employs rewards and punishments for behavior, emphasizing the effects of behavior on future behavior.

Negative Reinforcement

A process in behavioral psychology where the removal of an unpleasant stimulus strengthens a behavior.

Reciprocal Determinism

A concept in psychology positing that an individual's behavior is influenced by and influences their personal factors and the environment in a cyclical manner.

Vygotsky's Theory

A theory in psychology proposed by Lev Vygotsky, which emphasizes the fundamental role of social interaction in the development of cognition.