Problem

(a) Find the vertical and horizontal asymptotes. …

07:08

Problem 48 Hard Difficulty

(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 $

Answer

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

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Discussion

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Video Transcript

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WZ

Wen Z.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College