Please provide the correct answer Suppose f(x,y) = x2 + y2- 4x -4y + 3 How many

Question

Please provide the correct answer

Suppose f(x,y) = x2 + y2- 4x -4y + 3 How many critical points does f have in R2? If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. What is the maximum value of f on R2? If there is none, type N. What is the minimum value of f on R2? If there is none, type N.

Explanation / Answer

df/dx = 2x-4 = 0 -> x = 2

df/dy = 2y-4 = 0 -> y = 2

B)

D = 2*2 - 0 = 4

F)

min value is f(2,2) = -5

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