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) \(2 x y + 2 x ^ { 2 }\)

---

Definitions:

Consumer Price Index

An index measuring the change in the price level of a basket of consumer goods and services purchased by households.

Market Basket

A selected set of goods and services used to track changes in prices and measure inflation over time.

Widely Used

A term denoting something that is utilized by a large number of people or entities across various contexts.

Real Gross Domestic Product

A measure adjusted for inflation that shows the value of all products and services produced within an economy in a specific year.