(a) Find the intervals of increase or decrease.
(b) Find the local maximum and minimum values.
(c) Find the intervals of concavity and the inflection points.
(d) Use the information from parts $ (a) - (c) $ to sketch the graph.
Check your work with a graphing device if you have one.
$ S(x) = x - \sin x $, $ 0 \leqslant x \leqslant 4\pi $
a) increasing: $(0,2 \pi),(2 \pi, 4 \pi)$
b) no local min or max
c) $0 < x < \pi,$ concave up
$\pi < x < 2 \pi,$ concave down
$2 \p i < x < 3 \pi,$ concave up
$3 \pi < x < 4 \pi,$ concave down
d) SEE GRAPH
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