SOLUTION: Let f (x, y) = x2 + 2xy + 2y2 − 6y + 2. Find & identify all relative max’s and min’s.

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Question 634579: Let f (x, y) = x2 + 2xy + 2y2 − 6y + 2. Find & identify all relative max’s and
min’s.

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 
Hi, Previously Posted
f(x, y) = x^2 + 2xy + 2y^2 -6y + 2
∂ f/∂ x = 2x + 2y
∂ f/∂ y = 4y + 2x - 6
2x + 2y = 0
2x + 4y = 6
2y = 6
y = 3 and x = -3
= 2
= 2
= 4
D =
f(x,y) has minimum at (-3,3)
f(-3, 3) = 9 -18 +18 -18 + 2 = - 7
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