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:

Plane Joint

A type of synovial joint that allows for only gliding movement in various planes, commonly found in the carpals of the wrist.

Opposition

The movement that involves bringing the thumb and a finger together.

Reposition

The act or process of placing or arranging something in a different position.

Excursion

The movement of a structure or part away from its resting position, often used in the context of muscle movement or joint mobility.