Karush-Kuhn-Tucker Conditions

I want to minimise $\displaystyle -x_1^2 - x_2^2$ with the conditions that $\displaystyle 0<=x_1<=1, 0<=x_2<=1$ and I am supposed to confirm whether there is a minimum at point (1,0,0) or (1,1,1). Graphically, I can see the minimum is at (1,1,1), however, the KKT conditions also seem to get fulfilled at the point (1,0,0) which I can graphically is not the minimum. Any help appreciated!

Re: Karush-Kuhn-Tucker Conditions

Wait...why do you have points in 3-dimensions when you only have 2 optimization variables?