The correct answer is ts the forth one which is the contour plot of f(x,y) = x y.
The one above is f(x,y) = x2+y2 which has fxy=0 at the center.
The first one is just f(x,y)=g(x)
for some function of x, like x2, there is no y dependence so that fxy=0
there too. In the third case, fx is constant zero on the y axes as these are maxima.