Find the Linearization of the Function at the Given Point $$f ( x , y , z ) = \ln ( 6 x - 10 y - 4 z ) \text { at } \left( \frac { 1 } { 6 } , - \frac { 1 } { 10 } , - \frac { 1 } { 4 } \right)$$

question 60

Multiple Choice

Find the linearization of the function at the given point.
- $$f ( x , y , z ) = \ln ( 6 x - 10 y - 4 z ) \text { at } \left( \frac { 1 } { 6 } , - \frac { 1 } { 10 } , - \frac { 1 } { 4 } \right)$$

• A) \(L ( x , y , z ) = 3 x - 5 y - 2 z + \ln 3 - 1\)
• B) \(L ( x , y , z ) = 2 x - \frac { 10 } { 3 } y - \frac { 4 } { 3 } z + \ln 3 - 1\)
• C) \(\mathrm { L } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = 2 \mathrm { x } - \frac { 10 } { 3 } \mathrm { y } - \frac { 4 } { 3 } \mathrm { z } + \ln 2 - 1\)
• D) \(L ( x , y , z ) = 3 x - 5 y - 2 z + \ln 2 - 1\)

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Interest-Rate Effect

The change in spending and borrowing behavior in an economy due to a change in interest rates, often influencing total demand.

U.S. Economy

The economic system of the United States, characterized by a mixed economy with both private enterprise and government regulation.

Liquidity Preference

A theory that suggests individuals prefer to have their resources in liquid form to meet immediate demands for funds.

Irving Fisher

A renowned American economist known for his contributions to the theory of interest and the Fisher Equation.