For each of the following vector fields F , decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, $\nabla f = \mathbf{F}$) with $f(0,0) = 0$. If it is not conservative, type N.

A. $\mathbf{F} \left( x, y \right) = \left( 14 x+ 4 y \right) \mathbf{i} + \left( 4 x+ 10 y\right) \mathbf{j}$
$f \left( x, y \right) =$

B. $\mathbf{F} \left( x, y \right) = 7 y \mathbf{i} + 8 x \mathbf{j}$
$f \left( x, y \right) =$

C. $\mathbf{F} \left( x, y \right) = \left( 7 \sin y \right) \mathbf{i} + \left( 8 y+ 7 x \cos y \right) \mathbf{j}$
$f \left( x, y \right) =$

Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"

Your overall score for this problem is