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:

Covariance

An indicator showing the degree to which two variables fluctuate in unison.

Standard Error Of Estimate

A measure of the accuracy with which a sample distribution represents a population, particularly in regression analysis; it represents the average distance that the observed values deviate from the regression line.

Coefficient Of Correlation

A computation that assesses the power and orientation of a straight-line relation between two variables.

Causal Relationship

A connection between two variables where a change in one variable (the cause) leads to a change in another variable (the effect).