Which nonomial function has a minimum value y=5x^10 y=-4x^11 y=-x^12 y=6x^7

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