Find the absolute extrema of $f(x,y) = x^2 - xy + y^2$ on $|x| + |y| \leq 1$.
Hello. I am confused about how to solve the following Lagrange multiplier problem. It involves in inequality in the constraint so I began by finding the extrema within that domain by simply setting the first derivatives of f to 0, and finding that there is an extremum at (0, 0). However, the absolute values in the constraint confuse me when I try to use Lagrange multipliers. Can someone help me?
Find the absolute extrema of $f(x,y) = x^2 - xy + y^2$ on $|x| + |y| \leq 1$.
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