Answer
(A)
Work Step by Step
Notice that ${\bf{F}}$ are perpendicular to the level curves in (A) and (B). However, we see that the contours in (A) is increasing toward the right (because it is getting steeper from one level to the next one), whereas the contours in (B) is decreasing toward the right.
We observe that the vector field ${\bf{F}}$ is increasing as it moves to the right. This implies that a potential function for ${\bf{F}}$ must be increasing as it moves to the right. So, (A) in Figure 15 is the contour plot of a potential function for the vector field ${\bf{F}}$.
