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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.3, Problem 43E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
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Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
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Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
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Problem 51E
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Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
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Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

33-44

(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.

f ( θ ) = 2 cos θ + cos 2 θ ,   0 ≤ θ ≤ 2 π

To determine

(a)

To find:

The intervals of increase or decrease

Explanation

1) Concept:

Increasing or Decreasing test:

If f'x>0 then f is increasing

If f'x<0 then f is decreasing

2) Given:

fθ=2cos⁡θ+cos2⁡θ  0≤θ≤2π

3) Formula:

Sum and difference rule:

ddxfx±gx=ddxfx±ddx(gx)

4) Calculation:

Consider,

fθ=2cos⁡θ+cos2⁡θ  0≤θ≤2π

Differentiate with respect to θ,

f'θ=ddθ2cos⁡θ+cos2⁡θ

By using sum and difference rule,

f'θ=ddθ2cos⁡θ+ddθcos2⁡θ

=-2sin⁡θ-2cos⁡θsin⁡θ

= -2

To determine

(b)

To find:

Local maximum and local minimum values

To determine

(c)

To find:

Intervals of concavity and the inflection points

To determine

(d)

To sketch:

The graph by using information from part (a) – (c)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

CREDIT CARD OWNERSHIP A survey of 1020 adults aged 18-49 years found that 34 of them have no credit cards, 22 h...

Finite Mathematics for the Managerial, Life, and Social Sciences

For compactness, the drop-down wheels of a stretcher or gurney are folded under it as shown. In order for the b...

Elementary Geometry for College Students

Evaluating a Limit In Exercises 43-62, (a) describe the type of indeterminate form (if any) that is obtained by...

Calculus (MindTap Course List)

Evaluating a Function In Exercises 9-20, evaluate the function at the given values of the independent variables...

Multivariable Calculus

Finding a Limit In Exercises 43-46, find the limit. Use a graphing utility to verify your result. (Hint: Treat ...

Calculus

Queen City Cincinnati, Ohio, also known as the Queen City, has a population of approximately 298.000 and is the...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Identify each of the following angles as acute, obtuse, right, straight, or reflex. a. BAF b. ABF c. CBF d. DCA...

Mathematics For Machine Technology

The American Community Survey showed that residents of New York City have the longest travel times to get to wo...

Statistics for Business & Economics, Revised (MindTap Course List)

A student organization uses the proceeds from a particular soft-drink dispensing machine to financeits activiti...

Introduction To Statistics And Data Analysis

Use a graphing calculator to graph each equation and then find the x-coordinate of the x-intercept to the neare...

College Algebra (MindTap Course List)

Define a statistic and a parameter and explain the role that each plays in inferential statistics.

Research Methods for the Behavioral Sciences (MindTap Course List)

Describe the general characteristics of the survey research design.

Research Methods for the Behavioral Sciences (MindTap Course List)

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