Find all global solutions for the unconstrained problem
$\min_{x_1,x_2}f(x_1,x_2)=2x_1^2+x_2^2-2x_1x_2+x_1^3+x_1^4$
Now I'm a little bit confused. This is a problem from optimization class. Do I need to find the minima of this function or do I need to find all $f$ that have this minimum? In the first case I get the minimum at $(0,0)$ but since this problem asks for all solutions I'm not sure if there are more.
Any help would be appreciated!