Provide an Appropriate Response $\mathrm { P } _ { 0 }$

question 121

Multiple Choice

Provide an appropriate response.
-Find the direction in which the function is increasing most rapidly at the point $\mathrm { P } _ { 0 }$ . $f ( x , y , z ) = x y - \ln ( z ) , P _ { 0 } ( 1,2,2 )$

• A) \(\frac { 1 } { 21 } ( 4 \mathrm { i } + 2 \mathrm { j } - \mathrm { k } )\)
• B) \(\frac { 1 } { \sqrt { 21 } } ( 4 i - 2 j + k )\)
• C) \(\frac { 21 } { \sqrt { 21 } } ( 4 i + 2 j - k )\)
• D) \(\frac { 1 } { \sqrt { 21 } } ( 4 i + 2 j - k )\)

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Definitions:

Market Supply

Refers to the total amount of a product that producers are willing and able to sell at a given price over a certain period of time.

Agricultural Producers

Entities or individuals engaged in the cultivation of plants and rearing of animals for food, fiber, and other products used to sustain and enhance human life.

Welfare Change

A measure of changes in the economic well-being of individuals or communities, often resulting from policy decisions or economic events.

Tax Burden

The measure of taxes that individuals, businesses, or society as a whole must bear.