Which of the Following Could Represent a Function, F(x, Y) $\frac { \partial f } { \partial x } = 3 x y ( x y + 2 ) \quad \frac { \partial f } { \partial y } = x ^ { 2 } ( 2 x y + 3 )$

question 3

Multiple Choice

Which of the following could represent a function, f(x, y) , with first- order partial derivatives?
$\frac { \partial f } { \partial x } = 3 x y ( x y + 2 ) \quad \frac { \partial f } { \partial y } = x ^ { 2 } ( 2 x y + 3 )$

• A) \(x ^ { 3 } y ^ { 2 } + 3 x ^ { 2 } y - 6\)
• B) \(x y \left( x ^ { 2 } y + 3 \right)\)
• C) \(x ^ { 3 } y ^ { 2 } + 2 x ^ { 2 } y ^ { 3 } + 1\)
• D) \(x ^ { 2 } \left( x y ^ { 2 } + 3 \right)\)
• E) none of these

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Definitions:

Status Quo Effect

The tendency for individuals to prefer to keep things as they are rather than change, often driven by loss aversion and decision-making biases.

Invisible Hand

The tendency of competition to cause individuals and firms to unintentionally but quite effectively promote the interests of society even when each individual or firm is only attempting to pursue its own interests.

Behavioral Economics

A branch of economics focusing on how psychological, cognitive, emotional, cultural, and social influences impact the economic choices made by individuals and institutions.

Threat of Rejection

The fear or concern that one's ideas, actions, or presence will not be accepted by others.