Find the minimum value of \[2x^2 + 2xy + y^2 - 2x + 2y + 4\]over all real numbers $x$ and $y$.
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. :)
This figure should help: the green plane just touches the bottom of the orange function.
