Answer the Question $\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } )$

question 7

Multiple Choice

Answer the question.
-Consider a function $\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } )$ , where the independent variables are constrained to lie on the curve $\overrightarrow { \mathrm { r } } ( \mathrm { t } ) = \mathrm { x } ( \mathrm { t } ) \mathrm { i } +$ $y ( t ) j + z ( t ) k$ . What mathematical fact forms the basis for the method of Lagrange multipliers?

• A) \(\mathrm { f }\) approaches a local extremum as \(\lambda \rightarrow 0\).
• B)\({\nabla} f \cdot \nabla g=0\)
• C) \(\nabla g = 0\)
• D)\({\nabla} f \cdot \vec{v}=0\)

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Definitions:

Public Sector Unionization

The process or practice of organizing workers within public sector entities, such as government agencies or public schools, into labor unions to advocate for better wages, benefits, and working conditions.

Private Sector Unionization

The process or state of organizing workers into unions within privately owned businesses, as opposed to public sector or government employees.

Conspiracy Doctrine

A legal theory that views a combination of workers for the purpose of demanding better working conditions or wages as a criminal conspiracy.

National Labor Relations Act

A foundational U.S. law enacted in 1935 that protects the rights of employees to organize, engage in collective bargaining, and take collective action including strikes.