We learned this gradient vector stuff in class but after much struggling I just got the hang of it. I am not very flexible with it. All i know is that at a point the vector that points to the direction with highest rate of change is the gradient vector. I have a bit of confusion here. I found the gradient vector by squaring Fx and Fy then square rooting them to get gradient vector at point (x,y). However I found gradient vector at all those 4 points (4 quadrants) to be equal to sqrt2/e^2 which is strange to me. How can I tell from gradient vector if they are max or min? Using wolfram I got quadrant 2,4 are mins and 1,3 are max but I dont know how gradient tells whether the extrema are max or min.