Find the Maximum and Minimum Values Of $f ( x , y , z ) = x - 4 y + 6 z$

question 45

Essay

Find the maximum and minimum values of $f ( x , y , z ) = x - 4 y + 6 z$ subject to the constraint $g ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 53$ .

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Definitions:

Phytonadione

A form of vitamin K used clinically to prevent and treat bleeding disorders due to vitamin K deficiency.

Vitamin K

A fat-soluble vitamin essential for blood clotting and bone metabolism in the human body.

Prevent Bleeding

Measures or actions taken to reduce the risk of bleeding, which could involve medical interventions, lifestyle adjustments, or preventive care.

Prophylactic Eye Care

Preventive measures taken to protect the eyes from diseases, injuries, or other harmful conditions.