Using the Lagrange multipliers method I have to find the absolute maximum and minimum value of $f(x, y)=x^2+y^2-x-y+1$ in the unit disc.
So, I have to find the extremas of $f(x, y)=x^2+y^2-x-y+1$ subject to $x^2+y^2 \leq 1$, or not??
Do we not apply Lagrange multipliers method when we have a function $f(x,y)$ and a constaint $g(x, y)=0$??
So, shouldn't we have to have an equality at the constraint??
But in this case we have an inequality... What do we do??