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Find the Minimum Value of the Function f(x,y,z)=2x+y2zf ( x , y , z ) = 2 x + y - 2 z

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Find the minimum value of the function f(x,y,z) =2x+y2zf ( x , y , z ) = 2 x + y - 2 z subject to the constraint that x2+y2+z2=4x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4 .

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Definitions:

Frequency Count

Assessment in which the frequency of a particular behavior is counted.

Projective Test

is a type of psychological assessment that uses ambiguous stimuli to elicit responses that reveal aspects of an individual's personality.

Ambiguous Stimuli

Stimuli that can be understood in more than one way and often require interpretation by the individual.

Objective

Something that is based on factual evidence, uninfluenced by emotions or personal prejudices.

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