For What Value of the Constant $b$ Is There a Function $f ( x , y )$

question 6

Multiple Choice

For what value of the constant $b$ is there a function $f ( x , y )$ such that $\nabla f = b x ^ { 2 } y ^ { 2 } \mathbf { i } + x ^ { 3 } y \mathbf { j }$ ?

• A) \(0\)
• B) \(\frac { 1 } { 4 }\)
• C)\(\frac { 1 } { 2 }\)
• D)\(\frac { 3 } { 4 }\)
• E)\(1\)
• F)\(\frac { 5 } { 4 }\)
• G) \(\frac { 3 } { 2 }\)
• H)\(\frac { 7 } { 4 }\)

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Definitions:

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