(B) If there is a local minimum, what is the value of the discriminant D at that

ID: 2847404 • Letter: #

Question

(B) If there is a local minimum, 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.

Suppose

(A) How many critical points does have in ?

(B) If there is a local minimum, 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 on ? If there is none, type N.

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

f(x,y) = x^2 + y^2 - 6x - 10y + 4

fx(x,y) = 2x - 6 = 0

x = 3

fy(x,y) = 2y - 10 = 0

y = 5

There is one critical point at (3,5)

fxx = 2 > 0

fyy = 2

fxy = 0

fyx = 0

D(x,y) = fxx*fyy - fxy*fyx = (2)(2) - (0)(0) = 4

D(x,y) > 0 and fxx > 0, so this is a local min.

a. One critical point: (3,5)

b. 4

c. N

d. N

e. N

f. (3)^2 + (5)^2 - 6(3) - 10(5) + 4 = 9 + 25 - 18 - 50 + 4 = -30

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