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(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 maxc) $0 < x < \pi,$ concave up$\pi < x < 2 \pi,$ concave down$2 \p i < x < 3 \pi,$ concave up$3 \pi < x < 4 \pi,$ concave downd) SEE GRAPH

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

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(a) Find the intervals of increase or decrease.(b) Find the local maximu…