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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275347

Chapter 3.1, Problem 15E

Textbook Problem

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Approximating Critical Numbers In Exercises 13-16, approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown.

To determine

Whether the function in the graph given below has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these.

**Given:** The graph shown below:

**Explanation:**

Consider the provided graph and study it carefully,

Relative maximum is defined as if there is open interval *c* belongs to open interval *c* is maximum then, the value of function at *c* is called relative maximum.

Relative minimum is defined as if there is open interval *c* belongs to open interval *c* is minimum then, the value of function at *c* is called relative minimum.

The point where function gives maximum value over a domain is called absolute maximum.

Similarly, the point where function gives minimum value over the domain is called absolute minimum

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In Exercises 75-78, determine...Ch. 3.4 - True or False? In Exercises 75-78, determine...Ch. 3.4 - True or False? In Exercises 75-78, determine...Ch. 3.4 - True or False? 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The graph shows the temperature...Ch. 3.5 - Modeling Data The average typing speeds S (in...Ch. 3.5 - Modeling Data A heat probe is attached to the heat...Ch. 3.5 - Using the Definition of Limits at Infinity The...Ch. 3.5 - Using the Definition of Limits at Infinity The...Ch. 3.5 - Using the Definition of Limits at Infinity...Ch. 3.5 - Using the Definition of Limits at Infinity...Ch. 3.5 - Proof In Exercises 63-66, use the definition of...Ch. 3.5 - Proof In Exercises 63-66, use the definition of...Ch. 3.5 - Proof In Exercises 6366, use the definition of...Ch. 3.5 - Proof In Exercises 6366, use the definition of...Ch. 3.5 - Distance A line with slope m passes through the...Ch. 3.5 - Distance A line with slope m passes through the...Ch. 3.5 - Proof Prove that if p(x) = anxn + + a1x + a0 and...Ch. 3.5 - Proof Use the definition of infinite limits at...Ch. 3.6 - CONCEPT CHECK Analyzing the Graph of a Function...Ch. 3.6 - CONCEPT CHECK Analyzing a Graph Explain how to...Ch. 3.6 - CONCEPT CHECK Slant Asymptote Which type of...Ch. 3.6 - CONCEPT CHECK Polynomial What are the maximum...Ch. 3.6 - Matching In Exercises 5-8, match the graph of the...Ch. 3.6 - Matching In Exercises 5-8, match the graph of the...Ch. 3.6 - Matching In Exercises 5-8, match the graph of the...Ch. 3.6 - Matching In Exercises 5-8, match the graph of the...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 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 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 - Identifying Graphs In Exercises 51 and 52, the...Ch. 3.6 - Identifying Graphs In Exercises 51 and 52, 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 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 - EXPLORING CONCEPTS Sketching a Graph Sketch a...Ch. 3.6 - EXPLORING CONCEPTS Points of Inflection Is it...Ch. 3.6 - EXPLORING CONCEPTS Using a Derivative Let f'(t) 0...Ch. 3.6 - EXPLORING CONCEPTS Using a Derivative Let f(0) = 3...Ch. 3.6 - EXPLORING CONCEPTS A Function and Its Derivative...Ch. 3.6 - HOW DO YOU SEE IT? The graph of f is shown in 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 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Slant Asymptote In Exercises 7176, use a graphing...Ch. 3.6 - Investigation Let P(x0,y0) be an arbitrary point...Ch. 3.6 - Graphical Reasoning Identify the real numbers...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. 3.6 - True or False? In Exercises 8386, determine...Ch. 3.6 - True or False? In Exercises 8386, determine...Ch. 3.6 - True or False? In Exercises 8386, determine...Ch. 3.6 - True or False? In Exercises 8386, determine...Ch. 3.6 - Graphical Reasoning The graph of the first...Ch. 3.6 - Graphical Reasoning The graph of the first...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 - Investigation Consider the function f(x)=2xnx4+1...Ch. 3.6 - PUTNAM EXAM CHALLENGE Let f(x) be defined for axb....Ch. 3.7 - CONCEPT CHECK Writing In your own words, describe...Ch. 3.7 - CONCEPT CHECK Optimization Problems In your own...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 510, find two...Ch. 3.7 -
Finding Numbers In Exercises 5â€“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 13 and 14, find the...Ch. 3.7 - Minimum Perimeter In Exercises 13 and 14, find the...Ch. 3.7 - Minimum Distance In Exercises 15 and 16, find the...Ch. 3.7 - Minimum Distance In Exercises 15 and 16, find the...Ch. 3.7 -
17. Minimum Area A rectangular poster is to...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 - Minimum Distance Find the point on the graph of...Ch. 3.7 -
56. Minimum Distance Find the point on the graph...Ch. 3.7 - PUTNAM EXAM CHALLENGE Find, with explanation, the...Ch. 3.7 - PUTNAM EXAM CHALLENGE Find the minimum value of...Ch. 3.8 - Newtons Method In your own words and using a...Ch. 3.8 - Failure of Newtons Method Why does Newtons Method...Ch. 3.8 - Using Newtons Method In Exercises 3-6, calculate...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 - EXPLORING CONCEPTS Newtons Method What will be the...Ch. 3.8 - Newtons Method Does Newtons Method fail when the...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 - Approximating Reciprocals Use Newtons Method to...Ch. 3.8 - Approximating Reciprocals Use the result of...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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The graph shows the profit P...Ch. 3.9 - Pendulum The period of a pendulum is given by...Ch. 3.9 - Ohms Law A current of I amperes passes through a...Ch. 3.9 - Projectile Motion The range R of a projectile is...Ch. 3.9 - Surveying A surveyor standing 50 feet from the...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - EXPLORING CONCEPTS Comparing y and d y Describe...Ch. 3.9 - Using Defferentials Give a short explanation of...Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - True or False? In Exercises 49-53, determine...Ch. 3.9 - True or False? 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Using the Mean Value Theorem In Exercises 13-18,...Ch. 3 - Mean Value Theorem Can the Mean Value Theorem be...Ch. 3 - Using the Mean Value Theorem (a) For the function...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Intervals on Which a Function Is Increasing or...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Applying the First Derivative Test In Exercises...Ch. 3 - Motion Along a Line In Exercises 35 and 36, the...Ch. 3 - Motion Along a Line In Exercises 35 and 46, the...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Finding Points of Inflection In Exercises 3742,...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Using the Second Derivative Test In Exercises...Ch. 3 - Think About It In Exercises 49 and 50, sketch the...Ch. 3 - Think About It In Exercises 49 and 50, sketch the...Ch. 3 - Writing A newspaper headline states that "The rate...Ch. 3 - Inventory Cost The cost of inventory C depends on...Ch. 3 - Modeling Data Outlays for national defense D (in...Ch. 3 - Modeling Data The manager of a store recorded the...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 5564, find the limit,...Ch. 3 - Finding a Limit In Exercises 55-64, find the...Ch. 3 - Finding a Limit In Exercises 55-64, find the...Ch. 3 - Finding Horizontal Asymptotes Using Technology In...Ch. 3 - Finding Horizontal Asymptotes Using Technology In...Ch. 3 - Finding Horizontal Asymptotes Using Technology In...Ch. 3 - Finding Horizontal Asymptotes Using Technology In...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Analyzing the Graph of a Function In Exercises...Ch. 3 - Finding Numbers Find two positive numbers such...Ch. 3 - Minimum Distance Find the point on the graph of...Ch. 3 - Maximum Area A rancher has 400 feet of fencing...Ch. 3 - Maximum Area Find the dimensions of the rectangle...Ch. 3 - Minimum Length A right triangle in the first...Ch. 3 - Minimum Length The wall of a building is to be...Ch. 3 - Maximum Length Find the length of the longest pipe...Ch. 3 - Maximum Length A hallway of width 6 feet meets a...Ch. 3 - Maximum Volume Find the volume of the largest...Ch. 3 - Maximum Volume Find the volume of the largest...Ch. 3 - 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Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

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[âˆ’1, 1]
[âˆ’1, 1)
(âˆ’1, 1]
(âˆ’1, 1)

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By determining the limit of Riemann sums, the exact value of dx is
a) 7
b) 9
c)
d) 18

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