Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 1
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 8 What you’ll learn about Absolute (Global) Extreme Values Local (Relative) Extreme Values Finding Extreme Values …and why Finding maximum and minimum values of a function, called optimization, is an important issue in real-world problems.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Mean Value Theorem Physical Interpretation Increasing and Decreasing Functions Other Consequences …and why The Mean Value Theorem is an important theoretical tool to connect the average and instantaneous rates of change.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about First Derivative Test for Local Extrema Concavity Points of Inflection Second Derivative Test for Local Extrema Learning about Functions from Derivatives …and why Differential calculus is a powerful problem-solving tool precisely because of its usefulness for analyzing functions.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Examples from Mathematics Examples from Business and Industry Examples from Economics Modeling Discrete Phenomena with Differentiable Functions …and why Historically, optimization problems were among the earliest applications of what we now call differential calculus.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Linear Approximation Newton’s Method Differentials Estimating Change with Differentials Absolute, Relative, and Percent Change Sensitivity to Change …and why Engineering and science depend on approximation in most practical applications; it is important to understand how approximation techniques work.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Related Rate Equations Solution Strategy Simulating Related Motion …and why Related rate problems are at the heart of Newtonian mechanics; it was essentially to solve such problems that calculus was invented.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz for Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz for Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test Solutions
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