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)\({\nabla} f \cdot \vec{v}=0\)

---

Definitions:

Political Power

The capacity or authority to influence or control the behavior of others, especially in relation to the government or governance.

Equal Vote

The principle that every individual's vote carries the same weight in an electoral process, ensuring fairness and equality in democratic systems.

Colonial Era

A period in history marked by the establishment, expansion, and dominance of colonies by European powers in other parts of the world, often associated with exploration and economic exploitation.

Taxation

The process whereby governments impose charges on citizens and corporate entities to fund public expenses and services.