The question gives me a graph with a function and a vector and asks me to determine the sign of the directional derivative at various points. This part is easy. But then, it asks me to justify my answer using the dot product. How do I do that beyond simply saying "the dot product of the gradient and the vector is zero"?
I know this probably doesn't seem worthy of the holy Stack Exchange, but there are no Stack questions like it, the teacher decided not to release solutions, and he doesn't have office hours until the day before the exam so I'm totally stuck.