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Find the minimum value of \[2x^2 + 2xy + y^2 - 2x + 2y + 4\]over all real numbers $x$ and $y$.

 Dec 1, 2020
 #1
avatar+312 
+2

We can use the formula x=-b/(2a) and find the min/max value. After plugging in and solving we should have (0, y^2+2y+4) as our min/max value. Hope this helps. :)

 Dec 1, 2020
 #2
avatar+31693 
+2

This figure should help: the green plane just touches the bottom of the orange function.

 Dec 1, 2020

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