Suppose $f(x, y) = x^{2} + y^{2} - 4 x - 6 y + 1$

(A) How many critical points does $f$ have in $\mathbf{R}^{2}$?

(B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N.

(C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N.

(D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N.

(E) What is the maximum value of $f$ on $\mathbf{R}^{2}$? If there is none, type N.

(F) What is the minimum value of $f$ on $\bf{R}^{2}$? If there is none, type N.