Find the Absolute Maxima and Minima of the Function on the Given

question 365

Multiple Choice

Find the absolute maxima and minima of the function on the given domain.
- $$f ( x , y ) = x ^ { 2 } + y ^ { 2 } \text { on the diamond-shaped region } | x | + | y | \leq 4$$

• A) Absolute maximum: 16 at (4, 0), (-4, 0), (0, 4), and (0, -4); absolute minimum: 0 at (0, 0)
• B) Absolute maximum: 8 at 2, 2 , 2, - 2 , - 2, 2 , and - 2, - 2 ; absolute minimum: 0 at (0, 0)
• C) Absolute maximum: 16 at (4, 0) and (0, 4); absolute minimum: 0 at (-4, 0) and (0, -4)
• D) Absolute maximum: 16 at (4, 0), (-4, 0), (0, 4), and (0, -4); absolute minimum: 8 at 2, 2 , 2, - 2 , - 2, 2 , and - 2, - 2 ,

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Definitions:

Production Blocking

Reduction in individual creativity and productivity in brainstorming groups due to interruptions and turn-taking.

Social Loafing

The phenomenon where individuals exert less effort to achieve a goal when they work in a group compared to when they work alone.

Evaluation Apprehension

Evaluation apprehension is the anxiety or concern individuals may feel when they believe they are being judged or evaluated by others, affecting performance and behavior.

Production Blocking

A phenomenon in group brainstorming where the flow of ideas is inhibited because only one participant can speak at a time.