The function $g$ attains $\langle$takes/achieves$\rangle$ 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.
By computing the second derivative we note that $x=1$ is a maximum point for $f$.
This has a maximum value of 4 when $x=2$.
Then $V(x)$ is the maximum value of $J_x(v)$ 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
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