Find the Maximum Value of the Function $f ( x , y , z ) = 2 x + y - 2 z$

question 140

Multiple Choice

Find the maximum value of the function $f ( x , y , z ) = 2 x + y - 2 z$ subject to the constraint that $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ .

• A) \(- 4\)
• B) \(- 5\)
• C) \(- 6\)
• D) \(- 7\)
• E)4
• F)5
• G)6
• H)7

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Definitions:

Spinalis Cervicis

A neck muscle that is part of the spinalis muscle group, responsible for extending and stabilizing the cervical spine.

External Anal Sphincter

A muscle that surrounds the anus, controlling the expulsion of feces from the body.

Levator Ani Iliococcygeus

A component of the levator ani muscle, which supports the pelvic organs and helps in maintaining fecal continence.

External Urethral Sphincter

A circular muscle that controls urination by constricting or relaxing to allow the flow of urine from the bladder.