Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 5.3 Connecting f′ and f″ with the graph of f Applications of Derivatives Chapter 5.

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Presentation transcript:

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 5.3 Connecting f′ and f″ with the graph of f Applications of Derivatives Chapter 5

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2 Quick Review

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3 Quick Review

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4 Quick Review Solutions

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5 Quick Review Solutions

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 6 What you’ll learn about Intervals of increase or decrease Both First and Second Derivative Tests for local extrema Intervals of upward or downward concavity Points of inflection Identification of key features of functions and their derivatives …and why Differential calculus is a powerful problem-solving Tool precisely because of its usefulness for analyzing functions.

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 8 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 11 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 13 First Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 14 Example Using the First Derivative Test

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 15 Concavity

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 16 Concavity

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 17 Concavity Test

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 18 Example Determining Concavity

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 19 Point of Inflection

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 20 Example Finding Points of Inflection

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 21 Second Derivative Test for Local Extrema

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 22 Example Using the Second Derivative Test

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 23 Learning about Functions from Derivatives

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 24 Quick Quiz for Sections 5.1 – 5.3

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 25 Quick Quiz for Sections 5.1 – 5.3

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 26 Quick Quiz for Sections 5.1 – 5.3

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 27 Quick Quiz for Sections 5.1 – 5.3

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 28 Quick Quiz for Sections 5.1 – 5.3

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 29 Quick Quiz for Sections 5.1 – 5.3

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