Find the Absolute Extrema Of $$f ( x , y ) = 4 x ^ { 2 } + 2 y ^ { 2 } + 24 x - 8 \text { on the region }$$

question 110

Multiple Choice

Find the absolute extrema of $$f ( x , y ) = 4 x ^ { 2 } + 2 y ^ { 2 } + 24 x - 8 \text { on the region }$$ $$R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 49 \right\} .$$

• A) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( - 6 , - \sqrt { 13 } , 306 )\)
• B) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( 0,0 , - 8 )\)
• C) absolute minimum: \(( 0,0 , - 8 )\)
• absolute maximum: \(( 3,0,100 )\)
• D) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( 7,0,356 )\)
• E) absolute minimum: \(( - 3,0 , - 44 )\)
• absolute maximum: \(( - 6 , \sqrt { 13 } , 18 )\)

---

Definitions:

General Cognitive Ability

A measure of an individual's overall mental capacity, including memory, attention, and the ability to understand and process information.

Performance

The action of performing a task or function, commonly used to evaluate how well an activity is executed or a goal is achieved.

Emotional Intelligence

The ability to recognize, understand, and manage one's own emotions and those of others.

Job Performance

The level at which an individual executes their job responsibilities and tasks, often measured against pre-defined standards.