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)$\frac { 7 } { 4 }$

Question

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)$\frac { 7 } { 4 }$

Quizplus · Accepted Answer

The Answer of 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)$\frac { 7 } { 4 }$

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

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