Explain why f(x,y) = x has local extremum at infinitely many points. Select the correct answer below. O A. f, (x,y) and fy (x,y) are both equal to zero for x = 0 and y is any real number, meaning that each of these points represents a critical point. Since f(x,y) is nonnegative and equals 0 when x = 0, f has the local minimum 0 at each point of the y-axis. O B. fx (x,y) and fv (x,y) are always negative except at x = 0, where f(x,y) = 0, so f has the local maximum 0 at each point of the x-axis. O c. fx (x,y) and fv(x,y) are always negative except at x = 0, where f(x,y) = 0, so f has the local maximum 0 at each point of the y-axis. OD. f,(x,y) and fy(x,y) are both equal to zero for all points on the y-axis. Since AC -B