The question as presented, this is from Calculus Vol. II Section 8.14 #4
A differentiable scalar field $f$ has, at the point $(1,2)$, directional derivatives $+2$ in the direction toward $(2,2)$ and $−2$ in the direction toward $(1,1)$. Determine the gradient vector at $(1,2)$ and compute the directional derivative in the direction toward $(4,6)$.
Right off the bat, I think there must be a typo in the question because the directional derivatives in the direction of $(2,2)$ should be equal to the directional derivatives in the direction of $(1,1)$. So instead, I thought I would look at the answer for $(4,6)$ and try to find out what the typo was in the original problem. In the back of the book we have the answers as:
The gradient vector at $(1,2)$ is $(2,2)$, and the directional derivative in the direction toward $(4,6)$ is $\frac {14} 5$.
These don't seem to be consistent either, with each other or with the original question. Is this a series of typos, or am I misinterpreting something?