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:

Leadership Dimension

An element or aspect that contributes to the complex role of guiding or directing a group, organization, or nation.

Initiating Structure

Organizing and defining relationships in the group by activities such as assigning specific tasks, specifying procedures to be followed, scheduling work, and clarifying expectations of team members.

Self-fulfilling Prophecy

A belief or expectation that indirectly or directly causes itself to become true, through the behavior it inspires.

Initiating Structure

Leadership behavior that defines and organizes work roles and activities, and sets clear objectives.