Provide an Appropriate Response $f ( x , y )$ Given That

question 49

Multiple Choice

Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $f ( x , y )$ given that $\mathrm { f } _ { \mathrm { X } } = 8 \mathrm { x } - 4 \mathrm { y }$ and $\mathrm { f } _ { \mathrm { y } } = - 8 \mathrm { x } + 6 \mathrm { y }$ .

• A) Local maximum at \(\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)\)
• B) Local minimum at \(\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)\)
• C) Local minimum at \(( 0,0 )\)
• D) Saddle point at \(( 0,0 )\)

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Definitions:

Abdominal Thrust

A first aid procedure used to treat upper airway obstructions (or choking) by exerting pressure on the bottom of the diaphragm.

Obstructed Airway

A blockage in the passage through which air enters and leaves the lungs, which can be life-threatening.

Adults

refers to individuals who have reached maturity in terms of age, typically considered to be 18 years and older.

Finger Sweep

A first aid technique used to remove an obstructing object from the mouth of a choking individual when the object is visible and easily reachable.