Find a Function Of $f ( x , y )$ Such That

question 160

Multiple Choice

Find a function of $f ( x , y )$ such that $\nabla f = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$ .

• A) \(x ^ { 3 } y\)
• B) \(x ^ { 3 } y ^ { 2 }\)
• C)\(x ^ { 3 } / y\)
• D) \(x ^ { 3 } / y ^ { 2 }\)
• E) \(x ^ { 2 } y\)
• F) \(2 x ^ { 2 } y\)
• G) \(2 x y + x ^ { 2 }\)
• H) \(2 x y + 2 x ^ { 2 }\)

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Definitions:

Opportunity Cost

The expense associated with not choosing the second-best option when deciding.

Opportunity Cost

The value of the next best alternative foregone as a result of making a decision.

Point E

typically used in the context of graphs, it can represent a specific equilibrium point or any designated point of interest.

Point D

In the context of economics or finance, this term is incomplete without additional context to define its specific relevance.