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 .