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

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