The question is to determine for the vector field $$\vec{F} = P(x,y)\mathbf i+Q(x,y)\mathbf j$$below, determine if $Q_y$ is positive, negative or can't be determined at point $A$.
If we look at the vectors up and down point $A$, it doesn't seem like there is an obvious change in the magnitude of $y$ component of the vector. Let $A = (a_1,a_b)$, then when $x = a_1$, as $y$ increases, it does seem like the $x$ component of the vector field changes from positive to negative; the magnitude of the vectors do get larger. However, the magnitude of the vectors can get larger due to the increase in the magnitude of $x$ component. I can kind of tell that the $y$ components of the vectors do get larger, but the difference is so minute that I don't feel comfortable confirming that.
The answer to that question is: $Q_x > 0$ (not $Q_x \geq 0$. )
The other question also proves my intuition wrong. 
It asks whether $P_x$ at point $D$ is greater, equal or less than $0$. For the same reason, since the vectors along $y = D_y$ do point in the positive direction but I don't feel comfortable eyeballing the magnitude of $x$ components, I stated that there isn't enough information. The correct answer was $P_x > 0$.
I must be getting something wrong here. Can't someone please help?