Question 1
2 pts
Let $f(x, y)$ be a differentiable function of two variables. Is it
possible that for every direction $\mathbf{u}$ the directional derivative
$D_\mathbf{u} f(0, 0)$ is positive? If yes, then give an example and
explain why your example works. If not, then explain in detail
why this is impossible.
As with other questions of this kind, I am not asking for a
formal proof. Instead, I want to see a careful and cogent
explanation written in full sentences. If your answer involves
a computation, then you need to explain how your
computation answers the question.
