Thus, there are no relative extrema for F x. Other function values are listed. Thus, there are no relative extrema for G x. Therefore, there is a relative maximum at 0,1. We set the derivative equal to zero and solve the equation for x on the next page.
Thus, there are no relative extrema for f x. Next we find out where the derivative is zero. We use the information obtained to sketch the graph on the next page.
Otheee function values are listed below. Left to the student. Answers may vary, one such graph is: Answers may vary, one such graphhh Answers may vary, one such graphhh ntiation is: is: is: is: is: A line tangent to the curve at any point on either of these intervals has a positive slope. Thus, the function is increasing on the intervals for which the first derivative is positive.
Similarly, we see that on the intervals , and ,b c d e the function is decreasing. A line tangent to the curve at any point on either of these intervals has a negative slope. Thus, the function is decreasing on the intervals for which first derivative is negative. Letting t be years since and E be thousand of employees, we have the function: 3 2 Solve 2 ' 0 Since, E t is increasing on 1.
We divide the interval [ ]0, into two intervals, [ ]A: 0, and B: , Solve ' 0 0. We use it to divide the interval [ ]0,12 into two intervals: [ ]A: 0,6 and B: 6,12 Next, we test a point in each interval to determine the sign of the derivative. A: Test 20, ' 20 0. Thus, the longitude and latitude of the southernmost point at which the full eclipse could be view is We use the information obtained above to sketch the graph.
A possible graph is shown below. A possible grap below. A po is shown below. The h is shown interval ver the hermore it is 3. This g over the ver the again over s horizontal ssible graph There is a relative maximum at 0,1. There are relative minimums at 1,0 and 2,0. There is a relative maximum at 0,9. There is a relative minimum at 2,0.
The derivative exists for all values of x. There is a relative minimum at 1,0. The derivative does not exist at 1.
The graph is decreasing over the interval , 1. The graph is increasing over the interval 1. There are relative minimums at 1. The calculator returns When we try to run a quartic regression, the calculator returns a domain error. Therefore, the cubic regression fits best. Realistically, there would be some upper limit upon daily caloric intake. This leads us to believe that eating too many calories might shorten life expectancy.
In fact some calculators will return an error message when an attempt is made to fit a quartic function to the data. The greater the daily caloric intake, the lower the infant mortality.
In Exercises the function is given in equation form. The most accurate way to select an appropriate viewing window, one should first determine the domain, because that will help determine the x-range. For polynomials the domain is all real numbers, so we will typically select a x-range that is symmetric about 0. Next, you should find the critical values and make sure that your x-range contains them.
Finally, you should determine the x- intercepts and make sure the x-range includes them. To find the y-range, you should find the y-values of the critical points and make sure the y-range includes those values. You should also make sure that the y-range includes the y-intercept.
To avoid the calculations required to find the relative extrema and the zeros as described above, we can determine a good window by using the table screen on the calculator and observing the appropriate y- values for selected x-values. When the equations are somewhat complex, the best way to determine a viewing window is to use the table screen on the calculator and observing appropriate y-values for selected x-values.
You will need to set your table to accept selected x-values. Enter the table set up feature on your calculator and turn on the ask feature for your independent variable. This will allow you to enter an x-value and the calculator will return the y-value. You should make your ranges large enough so that all the data points will be easily viewed in the window. Total views On Slideshare 0. From embeds 0. Number of embeds 0. Downloads Shares 0. He is an avid sports fan and has authored books on hockey, baseball, and hiking.
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Out of print. Calculus and Its Applications, 10th Edition. Marvin L. If You're an Educator Download instructor resources Additional order info. The writing style addresses students in a direct, down-to-earth manner. The accessible, visual presentation helps students to easily navigate through the book. Artwork and figures are designed to complement the intuitive introductions to calculus concepts. Algebra diagnostic and review material is available for students who need to strengthen their basic skills.
Prerequisite Skills Diagnostic Test at the beginning of the text gives a convenient way to assess strengths and weaknesses. Answers at the back of the book direct students to the appropriate algebra remediation sections within the text.
Algebra review is provided at two levels: Appendix A addresses the basics, while Chapter R addresses functions, graphs, and models. Exponential and log functions are presented later in Chapter 3 , allowing students to focus more directly on the development of the derivative in Chapters 1 and 2.
Section support features give students the help they need without getting in the way. Objectives are listed at the beginning of each section, providing a roadmap of the material ahead.
Quick Check exercises after examples provide students with a way to check understanding at key junctures in the section. Section Summaries help students pull together the key ideas of the section prior to working the exercises.
Abundant section exercises give students the practice they need to understand and master the concepts. Technology is integrated but optional. The text allows for the utilization of graphing calculators, spreadsheets, and smartphone applications. All technology is clearly labeled and can be omitted as needs dictate.
Technology Connection features are designed with three distinct purposes: 1. Technology Connections Exercises are clearly labeled with an icon. These can be done individually or in a group setting. Test preparation material at the end of every chapter is designed to help students excel on tests. Chapter Summaries are redesigned to be more reference-like, helping students distill key ideas and prepare for tests.
All exercises are keyed back to specific sections in the chapter to help students know where to go for help and help instructors in making assignments. Chapter Tests are designed to mirror the tests typically administered in class. Real data , especially pertaining to the business world, helps students connect the concepts to their future careers.
Chapter Snapshots at the beginning of the chapter include an application to draw students into the concepts covered in the chapter. New to This Edition. This edition maintains all of the style and features that users have come to rely on, while reworking certain aspects to appeal to modern classrooms and students.
Quick Check exercises immediately follow examples, where appropriate, so students can assess their understanding before moving on in the book. Answers are provided following the section exercises. A Prerequisite Skills Diagnostic Test prior to Chapter R allows students and instructors to gauge the level of algebra preparedness before the course begins. Answers to the test reference Appendix A and Chapter R for review if necessary. This test is also available in MyMathLab for easy access at any time during the course.
Section summaries appear just prior to exercise sets, offering a quick recap of the key topics of the section before students begin their homework. Updated applications include more business-oriented examples and exercises. In particular, Section 5.
Data has been updated where necessary, so that problems use the most up-to-date information. Updated Technology Connections and Extended Technology Applications include coverage of the latest software, as well as widely used smartphone apps. End-of-chapter material has been streamlined so that it is easier to scan and refer to when studying. Three-dimensional art has been completely rerendered using the latest software to provide students with the best possible means for visualizing calculus concepts.
Based on input from users, Chapter 4 now begins with an introduction to the mechanics of antidifferentiation--the first step in the larger process of integration--serving as a bridge between differentiation Chapters 1, 2, and 3 and ntegration Chapters 4 and 5. This change allows students to focus on the mechanics of antidifferentiation before the concept of the area under a curve is introduced.
A detailed listing of content updates appears below. Chapter R Chapter R contains a general update of numerous problems involving real-world data.
Chapter 1 Chapter 1 contains 10 new examples designed to reinforce the main concepts and applications of limits, continuity, derivatives and the Chain Rule. Chapter 2 Sections 2. Chapter 3 This chapter reflects the tone of the rest of the book with new features, applications and updates of data in examples and exercises.
Chapter 4 This chapter has seen some significant rearrangement of the presentation of integration. Chapter 5 Chapter 5 begins with the discussion of consumer and producer surplus, which has been rewritten and the graphs re-rendered to illustrate some of the concepts more clearly. Chapter 6 Many new examples have been added to Chapter 6. Appendices In addition to the Review of Basic Algebra appendix, a new Regression on Excel appendix shows how regression can be calculated using Excel and later versions.
Functions, Graphs, and Models R. Differentiation 1. Applications of Differentiation 2. Exponential and Logarithmic Functions 3. Integration 4. Applications of Integration 5. Functions of Several Variables 6.
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