Find a Function $f ( x , y )$ Such That $\nabla f = \left( x ^ { 2 } + y \right) \mathbf { i } + ( x + y ) \mathbf { j }$

question 186

Multiple Choice

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

• A) \(\frac { 1 } { 3 } x ^ { 3 } + x y + y ^ { 2 }\)
• B) \(\frac { 1 } { 3 } x ^ { 3 } + \frac { 1 } { 2 } x y + \frac { 1 } { 2 } y ^ { 2 }\)
• C) \(\frac { 1 } { 3 } x ^ { 3 } + x y + \frac { 1 } { 2 } y ^ { 2 }\)
• D)\(\frac { 1 } { 3 } x ^ { 3 } + \frac { 1 } { 2 } x y + y ^ { 2 }\)
• E) \(\frac { 1 } { 2 } x ^ { 3 } + x y + y ^ { 2 }\)
• F)\(\frac { 1 } { 2 } x ^ { 3 } + \frac { 1 } { 2 } x y + \frac { 1 } { 2 } y ^ { 2 }\)
• G) \(\frac { 1 } { 2 } x ^ { 3 } + x y + \frac { 1 } { 2 } y ^ { 2 }\)
• H) \(\frac { 1 } { 2 } x ^ { 3 } + \frac { 1 } { 2 } x y + y ^ { 2 }\)

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