This is just a simple contour I download from the textbook. The original question is what is f(2,1), fx(2,1), and fy(2,1). I understand all of them with basic partial derivative knowledge. However, when I see what is fxx(2,1) or fyy(2,1). I cannot see those answers from the graph. Can someone give me a hint?
Since you already understand how fx and fy work in this contour. fxx and fyy just the change between fx and fy. Notice that, fxx is how fx change on the horizontal line (fyy just works similar way). You probably cannot see the change on fx and fy directly on the graph. I suggest you break the line(both x and y) near point(2,1) down to many small pieces on this cartesian graph. Mark fy and fx each small piece, then see how it changes from left to right and bottom to top. Those will be your fxx and fyy value. Be aware, fxy and fyx are different.
