We are dealing with monomial function so we just focus on end behavior.
5x¹⁰ has both ends going up so it would have minimum value
-4x¹¹ has one end going down and other end going up so no minimum value
-x¹² has both ends going down so it opens downward thus no minimum value. Just maximum.
6x⁷ has one ends going up and other going down so no minimum value.
So final answer is y = 5x¹⁰
