Calculus of a Single Variable
Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 3.6, Problem 1E

CONCEPT CHECK

Analyzing the Graph of a Function Name several of the concepts you have learned that are useful for analyzing the graph of a function.

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Chapter 3 Solutions

Calculus of a Single Variable

Ch. 3.1 - CONCEPT CHECK Minimum What does it mean to say...Ch. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - CONCEPT CHECK Critical Numbers Explain how to find...Ch. 3.1 - Prob. 6ECh. 3.1 - The Value of the Derivative at Relative Extrema In...Ch. 3.1 - The Value of the Derivative at Relative Extrema In...Ch. 3.1 - The Value of the Derivative at Relative Extrema In...Ch. 3.1 - The Value of the Derivative at Relative Extrema In...
Ch. 3.1 - The Value of the Derivative at Relative Extrema In...Ch. 3.1 - Prob. 12ECh. 3.1 - Approximating Critical Numbers In Exercises 13-16,...Ch. 3.1 - Approximating Critical Numbers In Exercises 13-16,...Ch. 3.1 - Approximating Critical Numbers In Exercises 13-16,...Ch. 3.1 - Prob. 16ECh. 3.1 - Finding Critical Numbers In Exercises 17-22, find...Ch. 3.1 - Finding Critical Numbers In Exercises 17-22, find...Ch. 3.1 - Finding Critical Numbers In Exercises 17-22, find...Ch. 3.1 - Finding Critical Numbers In Exercises 17-22, find...Ch. 3.1 - Finding Critical Numbers In Exercises 17-22, find...Ch. 3.1 - Prob. 22ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 24ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 26ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 28ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 30ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Finding Extrema on a Closed Interval In Exercises...Ch. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Finding Extrema Using Technology In Exercises 49...Ch. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Using Graphs In Exercises 57 and 58, determine...Ch. 3.1 - Using Graphs In Exercises 57 and 58, determine...Ch. 3.1 - Prob. 59ECh. 3.1 - Creating the Graph of a Function Graph a function...Ch. 3.1 - Power The formula for the power output P of a...Ch. 3.1 - Lawn Sprinkler A lawn spunkier is constructed in...Ch. 3.1 - Honeycomb The surface area of a cell in a...Ch. 3.1 - Highway Design In order to build a highway, it is...Ch. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Determine all real numbers a0 for which there...Ch. 3.2 - Rolle's Theorem In your own words, describe Rolles...Ch. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Writing In Exercises 3-6, explain why Rolle's...Ch. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Using Rolles Theorem In Exercises 7-10, find the...Ch. 3.2 - Prob. 8ECh. 3.2 - Using Rolles Theorem In Exercises 7-10, find the...Ch. 3.2 - Using Rolles Theorem In Exercises 7-10, find the...Ch. 3.2 - Using Rolle's Theorem In Exercises 11-24,...Ch. 3.2 - Prob. 12ECh. 3.2 - Using Rolle's Theorem In Exercises 11-24,...Ch. 3.2 - Using Rolle's Theorem In Exercises 11-24,...Ch. 3.2 - Using Rolle's Theorem In Exercises 11-24,...Ch. 3.2 - Prob. 16ECh. 3.2 - Using Rolle's Theorem In Exercises 11-24,...Ch. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Mean Value Theorem In Exercises 31 and 32, copy...Ch. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Writing In Exercises 33-36, explain why the Mean...Ch. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Using the Mean Value Theorem In Exercises 39-48,...Ch. 3.2 - Prob. 40ECh. 3.2 - Using the Mean Value Theorem In Exercises 39-48,...Ch. 3.2 - Using the Mean Value Theorem In Exercises 39-48,...Ch. 3.2 - Using the Mean Value Theorem In Exercises 39-48,...Ch. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 51ECh. 3.2 - Using the Mean Value Theorem In Exercises 49-52,...Ch. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Sales A company introduces a new product for which...Ch. 3.2 - Prob. 55ECh. 3.2 - EXPLORING CONCEPTS Rolles Theorem Let f be...Ch. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Temperature When an object is removed from a...Ch. 3.2 - Velocity Two bicyclists begin a race at 8:00 a.m....Ch. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Finding a Solution In Exercises 65-68, use the...Ch. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3.2 - Prob. 81ECh. 3.2 - Prob. 82ECh. 3.2 - Prob. 83ECh. 3.2 - Prob. 84ECh. 3.2 - Using the Mean Value Theorem Let 0ab. Use the Mean...Ch. 3.3 - CONCEPT CHECK Increasing and Decreasing Functions...Ch. 3.3 - Prob. 2ECh. 3.3 - Using a Graph In Exercises 3 and 4, use the graph...Ch. 3.3 - Using a Graph In Exercises 3 and 4, use the graph...Ch. 3.3 - Using a Graph In Exercises 5-10, use the graph to...Ch. 3.3 - Prob. 6ECh. 3.3 - Using a Graph In Exercises 5-10, use the graph to...Ch. 3.3 - Using a Graph In Exercises 5-10, use the graph to...Ch. 3.3 - Using a Graph In Exercises 5-10, use graph to...Ch. 3.3 - Prob. 10ECh. 3.3 - Intervals on Which a Function Is Increasing or...Ch. 3.3 - Prob. 12ECh. 3.3 - Intervals on Which a Function Is Increasing or...Ch. 3.3 - Prob. 14ECh. 3.3 - Intervals on Which a Function Is Increasing or...Ch. 3.3 - Prob. 16ECh. 3.3 - Intervals on Which a Function Is Increasing or...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Applying the First Derivative Test In Exercises...Ch. 3.3 - Applying the First Derivative Test In Exercises...Ch. 3.3 - Prob. 23ECh. 3.3 - Applying the First Derivative Test In Exercises...Ch. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Applying the First Derivative Test In Exercises...Ch. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Applying the First Derivative Test In Exercises...Ch. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Comparing Functions In Exercises 55 and 56, use...Ch. 3.3 - Think About It In Exercises 57-62, the graph of f...Ch. 3.3 - Prob. 58ECh. 3.3 - Think About It In Exercises 57-62, the graph of f...Ch. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Think About It In Exercises 57-62, the graph of f...Ch. 3.3 - EXPLORING CONCEPTS Transformations of Functions In...Ch. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - EXPLORING CONCEPTS Transformations of Functions In...Ch. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - HOW DO YOU SEE IT? Use the graph of f to (a)...Ch. 3.3 - Prob. 71ECh. 3.3 - Analyzing a Critical Number A differentiable...Ch. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - Prob. 77ECh. 3.3 - Prob. 78ECh. 3.3 - Trachea Contraction Coughing forces the trachea...Ch. 3.3 - Prob. 80ECh. 3.3 - Motion Along a Line In Exercises 81-84, the...Ch. 3.3 - Prob. 82ECh. 3.3 - Prob. 83ECh. 3.3 - Motion Along a Line In Exercises 81-84, the...Ch. 3.3 - Prob. 85ECh. 3.3 - Prob. 86ECh. 3.3 - Creating Polynomial Functions In Exercises 87-90,...Ch. 3.3 - Prob. 88ECh. 3.3 - Prob. 89ECh. 3.3 - Creating Polynomial Functions In Exercises 87-90,...Ch. 3.3 - Prob. 91ECh. 3.3 - Prob. 92ECh. 3.3 - Prob. 93ECh. 3.3 - Prob. 94ECh. 3.3 - Prob. 95ECh. 3.3 - Prob. 96ECh. 3.3 - Prob. 97ECh. 3.3 - Proof Prove the second case of Theorem 3.6.Ch. 3.3 - Prob. 99ECh. 3.3 - Prob. 100ECh. 3.3 - Prob. 101ECh. 3.4 - CONCEPT CHECK Test for Concavity Describe (he Test...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Using a Graph In Exercises 3 and 4, the graph of f...Ch. 3.4 - Determining Concavity In Exercises 5-16, determine...Ch. 3.4 - Prob. 6ECh. 3.4 - Determining Concavity In Exercises 5-16, determine...Ch. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Determining Concavity In Exercises 5-16, determine...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Determining Concavity In Exercises 5-16, determine...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Determining Concavity In Exercises 5-16, determine...Ch. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Finding Points of Inflection In Exercises 17-32,...Ch. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Finding Points of Inflection In Exercises 17-32,...Ch. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Sketching Graphs In Exercises 51 and 52, the graph...Ch. 3.4 - Think About It In Exercises 5356, sketch the graph...Ch. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Prob. 57ECh. 3.4 - How do you see It Water is running into the vase...Ch. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.4 - Prob. 61ECh. 3.4 - Prob. 62ECh. 3.4 - Aircraft Glide Path A small aircraft starts its...Ch. 3.4 - Prob. 64ECh. 3.4 - Average Cost A manufacturer has determined that...Ch. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Modeling Data The average typing speeds S (in...Ch. 3.4 - Prob. 69ECh. 3.4 - Linear and Quadratic Approximations In Exercises...Ch. 3.4 - Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.5 - CONCEPT CHECK Writing Describe in your own words...Ch. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Matching In Exercises 5-10, match the function...Ch. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Finding Limits at Infinity In Exercises 11 and 12,...Ch. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Prob. 18ECh. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Finding a Limit In Exercises 17-36, find the...Ch. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Finding Horizontal Asymptotes Using Technology In...Ch. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Finding a Limit In Exercises 43-46, find the...Ch. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - HOW DO YOU SEE IT? The graph shows the temperature...Ch. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 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 - Prob. 62ECh. 3.5 - Proof In Exercises 63-66, use the definition of...Ch. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.6 - CONCEPT CHECK Analyzing the Graph of a Function...Ch. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Matching In Exercises 5-8, match the graph of the...Ch. 3.6 - Prob. 6ECh. 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 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Analyzing the Graph of a Function In Exercises...Ch. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - Prob. 52ECh. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Prob. 55ECh. 3.6 - Prob. 56ECh. 3.6 - Prob. 57ECh. 3.6 - Prob. 58ECh. 3.6 - Prob. 59ECh. 3.6 - Prob. 60ECh. 3.6 - Prob. 61ECh. 3.6 - Prob. 62ECh. 3.6 - Prob. 63ECh. 3.6 - HOW DO YOU SEE IT? The graph of f is shown in the...Ch. 3.6 - Prob. 65ECh. 3.6 - Prob. 66ECh. 3.6 - Prob. 67ECh. 3.6 - Prob. 68ECh. 3.6 - Examining a Function In Exercises 69 and 70, use a...Ch. 3.6 - Prob. 70ECh. 3.6 - Prob. 71ECh. 3.6 - Prob. 72ECh. 3.6 - Prob. 73ECh. 3.6 - Prob. 74ECh. 3.6 - Prob. 75ECh. 3.6 - Prob. 76ECh. 3.6 - Investigation Let P(x0,y0) be an arbitrary point...Ch. 3.6 - Graphical Reasoning Identify the real numbers...Ch. 3.6 - Prob. 79ECh. 3.6 - Prob. 80ECh. 3.6 - Prob. 81ECh. 3.6 - Prob. 82ECh. 3.6 - Prob. 83ECh. 3.6 - Prob. 84ECh. 3.6 - Prob. 85ECh. 3.6 - Prob. 86ECh. 3.6 - Prob. 87ECh. 3.6 - Prob. 88ECh. 3.6 - Prob. 89ECh. 3.6 - Prob. 90ECh. 3.6 - Prob. 91ECh. 3.6 - Prob. 92ECh. 3.6 - Prob. 93ECh. 3.6 - Prob. 94ECh. 3.7 - CONCEPT CHECK Writing In your own words, describe...Ch. 3.7 - CONCEPT CHECK Optimization Problems In your own...Ch. 3.7 - Prob. 3ECh. 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 510, find two...Ch. 3.7 - Prob. 10ECh. 3.7 - Maximum Area In Exercises 11 and 12, find the...Ch. 3.7 - Prob. 12ECh. 3.7 - Minimum Perimeter In Exercises 13 and 14, find the...Ch. 3.7 - Prob. 14ECh. 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 - Minimum Area A rectangular poster is to contain...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 - Prob. 26ECh. 3.7 - Numerical, Graphical, and Analytic Analysis An...Ch. 3.7 - Prob. 28ECh. 3.7 - Maximum Volume A rectangular package to be sent by...Ch. 3.7 - Maximum Volume Rework Exercise 29 for a...Ch. 3.7 - Prob. 31ECh. 3.7 - Prob. 32ECh. 3.7 - Prob. 33ECh. 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 - Prob. 38ECh. 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 - Prob. 42ECh. 3.7 - Prob. 43ECh. 3.7 - Prob. 44ECh. 3.7 - Prob. 45ECh. 3.7 - Numerical, Graphical, and Analytic Analysis The...Ch. 3.7 - Prob. 47ECh. 3.7 - Prob. 48ECh. 3.7 - Prob. 49ECh. 3.7 - Prob. 50ECh. 3.7 - Prob. 51ECh. 3.7 - Maximum Area Consider a symmetric cross inscribed...Ch. 3.7 - Minimum Distance Find the point on the graph of...Ch. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.8 - Prob. 1ECh. 3.8 - Failure of Newtons Method Why does Newtons Method...Ch. 3.8 - Prob. 3ECh. 3.8 - Prob. 4ECh. 3.8 - Prob. 5ECh. 3.8 - Prob. 6ECh. 3.8 - Prob. 7ECh. 3.8 - Prob. 8ECh. 3.8 - Prob. 9ECh. 3.8 - Prob. 10ECh. 3.8 - Prob. 11ECh. 3.8 - Prob. 12ECh. 3.8 - Prob. 13ECh. 3.8 - Prob. 14ECh. 3.8 - Prob. 15ECh. 3.8 - Prob. 16ECh. 3.8 - Prob. 17ECh. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Prob. 20ECh. 3.8 - Prob. 21ECh. 3.8 - Prob. 22ECh. 3.8 - Prob. 23ECh. 3.8 - Failure of Newton's Method In Exercises 23 and 24,...Ch. 3.8 - Prob. 25ECh. 3.8 - Prob. 26ECh. 3.8 - Prob. 27ECh. 3.8 - Prob. 28ECh. 3.8 - Prob. 29ECh. 3.8 - Using Newtons Method Exercises 29-31 present...Ch. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - Prob. 33ECh. 3.8 - Prob. 34ECh. 3.8 - Prob. 35ECh. 3.8 - Prob. 36ECh. 3.8 - Prob. 37ECh. 3.8 - Prob. 38ECh. 3.8 - Prob. 39ECh. 3.8 - Prob. 40ECh. 3.8 - Prob. 41ECh. 3.8 - Prob. 42ECh. 3.9 - Prob. 1ECh. 3.9 - Prob. 2ECh. 3.9 - Prob. 3ECh. 3.9 - Prob. 4ECh. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Prob. 6ECh. 3.9 - Prob. 7ECh. 3.9 - Prob. 8ECh. 3.9 - Prob. 9ECh. 3.9 - Prob. 10ECh. 3.9 - Prob. 11ECh. 3.9 - Prob. 12ECh. 3.9 - Prob. 13ECh. 3.9 - Prob. 14ECh. 3.9 - Prob. 15ECh. 3.9 - Prob. 16ECh. 3.9 - Prob. 17ECh. 3.9 - Prob. 18ECh. 3.9 - Prob. 19ECh. 3.9 - Prob. 20ECh. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Prob. 22ECh. 3.9 - Prob. 23ECh. 3.9 - Prob. 24ECh. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Prob. 26ECh. 3.9 - Prob. 27ECh. 3.9 - Prob. 28ECh. 3.9 - Using Differentials In Exercises 29 and 30, use...Ch. 3.9 - Using Differentials In Exercises 29 and 30, use...Ch. 3.9 - Using Differentials In Exercises 31 and 32, use...Ch. 3.9 - Using Differentials In Exercises 31 and 32, use...Ch. 3.9 - Prob. 33ECh. 3.9 - Area The measurements of the base and altitude of...Ch. 3.9 - Prob. 35ECh. 3.9 - Prob. 36ECh. 3.9 - Stopping Distance The total stopping distance T of...Ch. 3.9 - Prob. 38ECh. 3.9 - Pendulum The period of a pendulum is given by...Ch. 3.9 - Prob. 40ECh. 3.9 - Projectile Motion The range R of a projectile is...Ch. 3.9 - Prob. 42ECh. 3.9 - Prob. 43ECh. 3.9 - Prob. 44ECh. 3.9 - Prob. 45ECh. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Prob. 47ECh. 3.9 - Prob. 48ECh. 3.9 - Prob. 49ECh. 3.9 - Prob. 50ECh. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - Prob. 52ECh. 3.9 - Prob. 53ECh. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Using Rolle's Theorem In Exercises 9-12, determine...Ch. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Prob. 75RECh. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Maximum Area A rancher has 400 feet of fencing...Ch. 3 - Prob. 82RECh. 3 - Minimum Length A right triangle in the first...Ch. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Prob. 98RECh. 3 - Prob. 99RECh. 3 - Prob. 100RECh. 3 - Prob. 101RECh. 3 - Prob. 1PSCh. 3 - Prob. 2PSCh. 3 - Relative Minimum Let f(x)=cx+x2 Determine all...Ch. 3 - Prob. 4PSCh. 3 - Prob. 5PSCh. 3 - Illumination The amount of illumination of a...Ch. 3 - Prob. 7PSCh. 3 - Areas of Triangles The line joining P and Q...Ch. 3 - Mean Value Theorem Determine the values a, b, and...Ch. 3 - Mean Value Theorem Determine the values a. b, c....Ch. 3 - Prob. 11PSCh. 3 - Proof (a) Prove that limxx2= (b) Prove that...Ch. 3 - Prob. 13PSCh. 3 - Prob. 14PSCh. 3 - Prob. 15PSCh. 3 - Prob. 16PSCh. 3 - Prob. 17PSCh. 3 - Prob. 18PSCh. 3 - Prob. 19PS
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