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 ,

Demonstrate an understanding of the von Neumann-Morgenstern utility function and its implications for expected utility.

Calculate the expected utility of given scenarios and identify the option that maximizes utility.

Understand the significance of probability in decision-making under uncertainty.

Assess the impact of risk aversion on gambling and betting decisions.

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