Find the Directional Derivative of the Function $f ( x , y ) = ( x + 6 ) e ^ { y }$

question 58

Multiple Choice

Find the directional derivative of the function $f ( x , y ) = ( x + 6 ) e ^ { y }$ at the point $P ( 7,0 )$ in the direction of the unit vector that makes the angle $\theta = \frac { \pi } { 2 }$ with the positive $x$ -axis.

• A) \(6 e ^ { 7 }\)
• B) 13
• C) 1
• D) \(e ^ { 7 }\)

Understand the concept and significance of the production possibilities frontier (PPF).

Define economic growth and identify factors contributing to it.

Understand the relationship between employment status and the position on the PPF.

Recognize the dynamics of resources in economic growth and the role of opportunity cost.

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Definitions:

Consumer Price Index

An index measuring the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.

Competitive

A market situation wherein there are many sellers and buyers, leading to prices that reflect supply and demand.

Geographic Extent

The physical or virtual area over which a study, policy, or market operates, often influencing its scope and impact.

Real Price

The price of a good or service adjusted for inflation, reflecting its purchasing power relative to a specific base year.