This is not the intention of the exercise. They do not want you to indentify the graph. To explain how they want you to do it, I will do 5(a).

It asks to find fx(1,2)
, i.e. how f changes as you move in the x direction from the point (1,2). If you go in the positive x direction from the pink spot which represents (1,2), then you can see that the z co-ordinate (i.e. f value) increases. So the sign of fx

is positive at this point.

Similarly you can do 5(b), 6(a) and 6(b).

When it asks to find fxx(−1,2)
, this means “the rate at which fx is changing as you advance in the x direction at this point”. At that point, fx is negative, since the graph is going downwards as you advance in the positive x direction. But fx is increasing, since the “negative slope” is becoming less steep, like going from gradient of −2 to −1. So fxx

is positive.

Similarly you can do 7(b).

When the two letters are different, you need to find “the rate at which fx
changes as you move in the positive y direction”. This, combined with the method for question 7, is how to do 8(a) and 8(b).