The Surface of a Certain Lake Is Represented by a Region

question 9

Essay

The surface of a certain lake is represented by a region in the $x y$ -plane such that the depth under the point corresponding to $( x , y )$ is $f ( x , y ) = 300 - 2 x ^ { 2 } - 3 y ^ { 2 }$ . Zeke the dog is at the point $( 3,2 )$ .(a) In what direction should Zeke swim in order for the depth to decrease most rapidly?
(b) In what direction would the depth remain the same?

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Definitions:

GDP

Gross Domestic Product, the total market value of all final goods and services produced within a country in a specific time period.

Natural Rate

The natural rate typically signifies the unemployment rate that maintains a steady inflation rate over time, also known as the natural rate of unemployment.

Short-run Ups

Temporary or brief increases in economic indicators or market performance.

Standard of Living

The level of wealth, comfort, material goods, and necessities available to a person, group, or nation.