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) About Me  (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

f%5Bxx%5D = 2

f%5Bxy%5D = 2

f%5Byy%5D = 4

D = 2%2A4+-+2%5E2+=+4+%3E+0 

f(x,y) has minimum at (-3,3) 

f(-3, 3) = 9 -18 +18 -18 + 2 = - 7