Given the image, state if point A is a maximum, minimum, saddle point or none of them

Question

I am asked the following question:

The image shows the level curves of an unknown function $f(x,y)$. What can we state about the point A?

a) It´s a maximum

b) It´s a minimum

c) It´s a saddle point

d) None of the above

Im prone to saying none of the above sine, for me, it looks like a discontinuity of the function (as if it were increasing up until infinity.

Is my reasoning correct?

EDIT: This actually is from a book. If the question is not well-made, I want to have arguments to contact the writer, so I am very interested to know if thats the case.

Answer 1

I think it's safe to assume that the function is continuous (since plotting level sets can't tell you much of anything about a function that isn't continuous), but even so, without knowing the values of the function on the level sets in the figure, you can't say anything, except that the point is a (perhaps non-isolated) critical point. It's a good exercise to think of function values on the level sets for which each of those answers is the correct one.