Find the Linearization of the Function at the Given Point $\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { e } ^ { 5 \mathrm { x } - 8 \mathrm { y } + 3 \mathrm { z } }$

question 30

Multiple Choice

Find the linearization of the function at the given point.
- $\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { e } ^ { 5 \mathrm { x } - 8 \mathrm { y } + 3 \mathrm { z } }$ at $( 0,0,0 )$

• A) \(L ( x , y , z ) = \frac { 5 } { 2 } x - 4 y + \frac { 3 } { 2 } z + 1\)
• B) \(L ( x , y , z ) = 5 x - 8 y + 3 z\)
• C) \(L ( x , y , z ) = 5 x - 8 y + 3 z + 1\)
• D) \(L ( x , y , z ) = \frac { 5 } { 2 } x - 4 y + \frac { 3 } { 2 } z\)

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Definitions:

Differential Cost

is the change in a company's cost of producing goods or services under two different action alternatives, essentially the cost difference between two choices.

Unused Capacity

The available but not utilized production ability of a company which could potentially generate revenue if employed.

Unit Cost

The cost incurred to produce, store, or acquire one unit of a product, calculated by dividing the total cost by the number of units.

Differential Cost

The difference in cost between two alternative decisions or scenarios.