Suppose f(x,y)=x2+y2−2x−2y+1f(x,y)=x2+y2−2x−2y+1 (A) How many critical points does ff have in R2R2? (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 ff on R2R2? If there is none, type N. (F) What is the minimum value of ff on R2R2? If there is none, type N

Question

Suppose f(x,y)=x2+y2−2x−2y+1f(x,y)=x2+y2−2x−2y+1

(A) How many critical points does ff have in R2R2?

(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 ff on R2R2? If there is none, type N.

(F) What is the minimum value of ff on R2R2? If there is none, type N.

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