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

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) $\frac { 7 } { 4 }$