$X$ denotes the set $\{ f \in C[-1,1] | f ~ is~ continuous~ differentiable~ on~ [0,1]\}$,
$Y$ denotes $\{ f \in X | f ~satisfies~ $f '(t) = f(t-1)$~ on~ [0,1]\}$.
For any $f\in X$, does there exists an $h\in Y$ such that $\max|f(t) - h(t) | =d (f, Y)$? where $d(f,Y)= \inf_{y\in Y} \max_{t\in [-1,1]}|f(t) - y(t)|$