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:

Self-discrepancy

The gap between one's actual self and ideal or ought selves, which can influence emotions and behaviors.

Social Comparison

The process of evaluating oneself by comparing with others, often to assess one's abilities, status, or opinions.

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This refers to the process of increasing in size, volume, quantity, or scope.

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Pertains to aspects of health and wellbeing, including physical, mental, and social factors.