The likelihood function is

Where that is the first order stat.

YOU do not differentiate this. You want the max wrt u.

The max occurs when u is as large as possible since u is in the numerator.

But the largest this can be is , otherwise you have ZERO for that indicator.

HENCE the MLE of u is .

AS for the MOM, I get 2u as the E(X), so get

or or .