Determine whether each of the following vector fields \vec{f} is a gradient field or not.

if it is a gradient field, enter a potential function for it. if it is not a gradient field, enter none.

(a) if \vec{f}(x, y) = (x + 3) \vec{i} + (2 y + 3) \vec{j}, then f(x, y) =

(b) if \vec{f}(x, y) = (2 x + 3 y)\vec{i} + (3 x + 2 y)\vec{j}, then f(x, y) =

(c) if \vec{f}(x, y) = \langle -4 y, 4x \rangle, then f(x, y) =