For Each of the Following Functions, Find the Critical Point $f ( x , y ) = 4 x ^ { 2 } + 3 x - 5 y ^ { 2 } - 8 y + 7$

question 245

Essay

For each of the following functions, find the critical point, if there is one, and determine if it is a local maximum, local minimum, saddle point, or otherwise.(a) $f ( x , y ) = 4 x ^ { 2 } + 3 x - 5 y ^ { 2 } - 8 y + 7$ (b) $f ( x , y ) = - 2 x ^ { 2 } + 7 x - 7 y ^ { 2 } + 4 y + 9$ (c) $f ( x , y ) = 3 x ^ { 2 } - 5 y + 4 y ^ { 2 } + 12 x - 11$ (d) $f ( x , y ) = 2 y ^ { 2 } + 7 x + 17 y + 12$

---

Definitions:

Norming Stage

A phase within group development where members resolve conflicts, enhance unity and cohesion, and start to work more effectively as a unit.

Open Communication

The practice of freely exchanging information, ideas, and feelings in a straightforward and transparent manner, fostering understanding and trust.

Initial Norms

The starting rules, values, or standards of behavior that are accepted within a group or society.

Work Schedule

A plan that outlines the days and hours designated for work activities, often used to manage an employee's time during the workweek.