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10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 3.6, Problem 5E

Textbook Problem

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Analyzing the Graph of a Function In Exercises 9-36, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.

To determine

**To graph:** The function

**Given:** The function

**Graph:**

The function being a polynomial has a domain as all the real numbers except for

The function can’t take the value -3 and thus the range of the function would be

Now by equating *x* to zero respectively we will find the *x* and *y* intercepts

The *x*-intercept is *y*-intercept is

Now the function does have a vertical asymptote as

Also,

This implies that the function has a horizontal asymptote as

Now, differentiate the function with respect to *x* and equate it to zero to obtain the critical points.

Clearly, this can never be zero and is not defined at

This gives two test intervals

Let

The function is decreasing in this interval.

Let

The function is decreasing in this interval

Calculus

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Average Cost A business has a cost of C = 0.5x...Ch. 3.5 - Physics Newtons First Law of Motion and Einsteins...Ch. 3.5 - HOW DO YOU SEE IT? 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In Exercises 103 and 104, determine...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Matching In Exercises 14, match the graph of f in...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Analyzing the Graph of a Function InExercises...Ch. 3.6 - Analyzing the Graph of a Function InExercises...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - Analyzing the Graph of a Function Using Technology...Ch. 3.6 - WRITING ABOUT CONCEPTS Using a Derivative Let...Ch. 3.6 - Using a Derivative Let f(0) = 3 and 2 f'(x) 4...Ch. 3.6 - Identifying Graphs In Exercises 51 and 52, the...Ch. 3.6 - Identifying Graphs In Exercises 51 and 52, the...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Horizontal and Vertical Asymptotes In Exercises...Ch. 3.6 - Examining a Function In Exercises 69 and 70, use a...Ch. 3.6 - Examining a Function In Exercises 69 and 70, use a...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning In Exercises 5356, use the...Ch. 3.6 - Graphical Reasoning Consider the function...Ch. 3.6 - Graphical Reasoning Consider the function f(x) =...Ch. 3.6 - Graphical Reasoning Identify the real numbers...Ch. 3.6 - HOW DO YOU SEE IT? The graph of f is shown in the...Ch. 3.6 - Investigation Let P(x0,y0) be an arbitrary point...Ch. 3.6 - Investigation Consider the function f(x)=2xnx4+1...Ch. 3.6 - Graphical Reasoning Consider the function...Ch. 3.6 - Graphical Reasoning Consider the function...Ch. 3.6 - Slant Asymptotes In Exercises 91 and 92, the graph...Ch. 3.6 - Slant Asymptotes In Exercises 91 and 92, the graph...Ch. 3.6 - PUTNAM EXAM CHALLENGE Let f(x) be defined for axb....Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.6 - Think About It In Exercises 7982, create a...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis Find...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis An...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 38, find two positive...Ch. 3.7 -
Finding Numbers In Exercises 5–10, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Maximum Area In Exercises 11 and 12, find the...Ch. 3.7 - Maximum Area In Exercises 11 and 12, find the...Ch. 3.7 - Minimum Perimeter In Exercises 11 and 12, find the...Ch. 3.7 - Minimum Perimeter In Exercises 13 and 14, find the...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Distance In Exercises 1316, find the point...Ch. 3.7 - Minimum Area A rectangular page is to contain 30...Ch. 3.7 - Minimum Area A rectangular page is to contain 36...Ch. 3.7 - Minimum Length A farmer plans to fence a...Ch. 3.7 - Maximum Volume A rectangular solid (with a square...Ch. 3.7 - Maximum Area A Norman window is constructed by...Ch. 3.7 - Maximum Area A rectangle is bounded by the x- and...Ch. 3.7 - Minimum Length and Minimum Area A right triangle...Ch. 3.7 - Maximum Area Find the area of the largest...Ch. 3.7 - Maximum Area A rectangle is bounded by the x-axis...Ch. 3.7 - Maximum Area Find the dimensions of the largest...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis An...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis A...Ch. 3.7 - Maximum Volume A rectangular package to be sent by...Ch. 3.7 - Maximum Volume Rework Exercise 29 for a...Ch. 3.7 - EXPLORING CONCEPTS Surface Area and Volume A...Ch. 3.7 - EXPLORING CONCEPTS Area and Perimeter The...Ch. 3.7 - Minimum Surface Area A solid is formed by...Ch. 3.7 - Minimum Cost An industrial tank of the shape...Ch. 3.7 - Minimum Area The sum of the perimeters of an...Ch. 3.7 - Maximum Area Twenty feet of wire is to be used to...Ch. 3.7 - Beam Strength A wooden beam has a rectangular...Ch. 3.7 - Minimum Length Two factories are located at the...Ch. 3.7 - Minimum Cost An offshore oil well is 2 kilometers...Ch. 3.7 - Illumination A light source is located over the...Ch. 3.7 - Minimum Time A man is in a boat 2 miles from the...Ch. 3.7 - Minimum Time The conditions are the same as in...Ch. 3.7 - Minimum Distance Sketch the graph of f(x)=22sinx...Ch. 3.7 - Minimum Time When light waves traveling in a...Ch. 3.7 - Maximum Volume A sector with central angle is cut...Ch. 3.7 - Numerical, Graphical, and Analytic Analysis The...Ch. 3.7 - Maximum Profit Assume that the amount of money...Ch. 3.7 - HOW DO YOU SEE IT? The graph shows the profit P...Ch. 3.7 - Minimum Distance In Exercises 49-51, consider a...Ch. 3.7 - Minimum Distance In Exercises 49-51, consider a...Ch. 3.7 - Minimum Distance In Exercises 49-51, consider a...Ch. 3.7 - Maximum Area Consider a symmetric cross inscribed...Ch. 3.7 - PUTNAM EXAM CHALLENGE Find, with explanation, the...Ch. 3.7 - PUTNAM EXAM CHALLENGE Find the minimum value of...Ch. 3.8 - Using Newton's Method In Exercises 14, complete...Ch. 3.8 - Using Newton's Method In Exercises 3-6, calculate...Ch. 3.8 - Using Newtons Method In Exercises 3-6, calculate...Ch. 3.8 - Using Newtons Method In Exercises 3-6, calculate...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Using Newton's Method In Exercises 7-16, use...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Using Newton's Method Consider the function...Ch. 3.8 - Using Newton's Method Repeat the steps in Exercise...Ch. 3.8 - Failure of Newton's Method In Exercises 23 and 24,...Ch. 3.8 - Failure of Newton's Method In Exercises 23 and 24,...Ch. 3.8 - Fixed Point In Exercises 25-26, approximate the...Ch. 3.8 - Fixed Point In Exercises 25 and 26, approximate...Ch. 3.8 - Approximating Reciprocals Use Newtons Method to...Ch. 3.8 - Approximating Reciprocals Use the result of...Ch. 3.8 - Using Newtons MethodExercises 2931 present...Ch. 3.8 - Using Newtons Method Exercises 29-31 present...Ch. 3.8 - Using Newtons Method Exercises 29-31 present...Ch. 3.8 - HOW DO YOU SEE IT? For what value(s) will Newtons...Ch. 3.8 - Mechanics Rule The Mechanics Rule for...Ch. 3.8 - Approximating Radicals (a) Use Newtons Method and...Ch. 3.8 - Newton's Method In your own words and using a...Ch. 3.8 - Crime The total number of arrests T (in thousands)...Ch. 3.8 - True or False? In Exercises 37-40, determine...Ch. 3.8 - True or False? In Exercises 3740, determine...Ch. 3.8 - True or False? In Exercises 3740, determine...Ch. 3.8 - True or False? 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Logarithmic Differentiation In Exercises 65-68, use logarithmic differentiation to find dy/dx. y=xx1

Calculus of a Single Variable

In Exercises 9-18, evaluate CFdr using the Fundamental Theorem of Line Integrals. Use a computer algebra system...

Calculus: Early Transcendental Functions (MindTap Course List)

Find the perimeter of the room in Exercise 35.

Elementary Geometry for College Students

An unbiased coin is tossed five times. In Exercises 14, find the probability of the given event. The coin lands...

Finite Mathematics for the Managerial, Life, and Social Sciences

Using the Second Partial TestIn Exercises 7984, find all relative extrema and saddle points of the function. Us...

Multivariable Calculus

True or False:
By the Integral Test, converges.

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

True or False:
If converges and converges, then converges.

Study Guide for Stewart's Multivariable Calculus, 8th

Describe the three ways identified in the text to find or develop a new research idea from existing research re...

Research Methods for the Behavioral Sciences (MindTap Course List)

consider the following hypothesis test: H0: 20 Ha: 20 A sample of 50 provided a sample mean of 19.4. The po...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

PRACTICE PROBLEMS Solve by factoring x33x2+3x1=0.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Construct a stem-and-leaf display for the following data. Use a leaf unit of 10.

Essentials Of Statistics For Business & Economics

Find the center and radius and sketch the graph of the circle given by x2+y22x2y+1=0

Mathematics: A Practical Odyssey

In a survey of 100 people who had recently purchased motorcycles, data on the following variables were recorded...

Introduction To Statistics And Data Analysis

Find the fraction or decimal equivalents of these numbers using the decimal equivalent table. 9. 1132

Mathematics For Machine Technology

Testing for Functions In Exercises 9 and 10, which sets of ordered pairs represent functions from A to B ? Expl...

College Algebra

Simplify each expression. Write all answer without using negative exponents. Assume that all variables are rest...

College Algebra (MindTap Course List)

The price per share of stock for a sample of 25 companies was recorded at the beginning of 2012 and then again ...

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

Describe, compare, and contrast the five research strategies (descriptive, correlational, experimental, quasi-e...

Research Methods for the Behavioral Sciences (MindTap Course List)

In 5-7, show that the two drawings represent the same graph by labeling the vertices and edges of the right-han...

Discrete Mathematics With Applications