Use Lagrange Multipliers to Find the Maximum and the Minimum $f$

question 108

Short Answer

Use Lagrange multipliers to find the maximum and the minimum of $f$ subject to the given constraint(s).
$$f ( x , y ) = x y z ; \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 3$$

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Definitions:

Critical Period

A specific time during development when the presence or absence of certain experiences has a profound impact on the formation of abilities or characteristics.

Social Cognitive Theory

A theory that posits that learning occurs in a social context with a dynamic and reciprocal interaction of the person, environment, and behavior.

Classical Conditioning

An educational method where a response initially triggered by a second stimulus comes to be triggered by the first stimulus alone, due to the repeated pairing of both stimuli.

Classical Conditioned

A learning process that pairs a neutral stimulus with a response-producing stimulus, leading to the neutral stimulus eliciting the response on its own.