Solve the Given Problem by Using Substitution $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4$

question 34

Multiple Choice

Solve the given problem by using substitution.
Find the minimum value of $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4$ subject to $y = 2 x$ .

• A) \(f _ { \min } = - 5\)
• B) \(f _ { \min } = - 4\)
• C) \(f _ { \min } = - 3\)
• D) \(f _ { \min } = - 2\)
• E) \(f _ { \min } = - 6\)

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Definitions:

Gifted

Describing individuals who possess above-average intelligence or talents in specific areas.

Psychological

Pertaining to the mind or mental processes, involving aspects of cognitive, emotional, and social behavior and functions.

Personality Problems

Difficulties in the enduring pattern of thinking, feeling, and behaving that significantly deviate from the expectations of one's culture, causing distress or impaired functioning.

Problem Solving

Process of cognition that occurs when a goal must be reached by thinking and behaving in certain ways.