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Answer
$f(x) = |x - 1| + |x - 5|$
$f(x) = \left\{ \begin{array}{l} - (x - 1) - (x - 5),\,\,\,x < 1\\\,\,\,\,(x - 1) - (x - 5),\,\,\,1 < x < 5\\\,\,\,\,\,\,\,x - 1 + x - 5,\,\,\,\,x > 5\end{array} \right.$
$f(x) = \left\{ {\begin{array}{*{20}{c}}{6 - 2x,}&{x < 1}\\{4\,\,\,\,\,\,,}&{1 < x < 5}\\{2x - 6,}&{x > 5}\end{array}} \right.$
$\because x = 3 \in (1,\,5)$,
For $x = 3, f(x) = 4, f\ '(x) = 0$.
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