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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