The function g attains <takes/achieves> its maximum at x=5.
For example, F reaches a relative maximum of 5.2 at about x=2.1.
Now (c) asserts only that the overall maximum of f on U is attained at some point of the boundary.
This has a maximum value of 4 when x=2.
Then V(x) is the maximum value of Jx(v) over all controls v.
Let q be the maximum number of variables occurring in...... [Note the double r in occurring.]
vectors in V at maximum distance from v
the maximum possible density