Chapter2

Chapter2 - Chapter 2 Applications of the Derivative

This preview shows pages 1–14. Sign up to view the full content.

Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 1 of 107 Chapter 2 Applications of the Derivative

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 2 of 107 Describing Graphs of Functions The First and Second Derivative Rules The First and Second Derivative Tests and Curve Sketching Curve Sketching (Conclusion) Optimization Problems Further Optimization Problems Applications of Derivatives to Business and Economics Chapter Outline
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 3 of 107 § 2.1 Describing Graphs of Functions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 4 of 107 Increasing and Decreasing Functions Relative and Absolute Extrema Changing Slope Concavity Inflection Points x - and y -Intercepts Asymptotes Describing Graphs Section Outline
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 5 of 107 Increasing Functions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 6 of 107 Decreasing Functions
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 7 of 107 Relative Maxima & Minima

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 8 of 107 Absolute Maxima & Minima
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 9 of 107 Changing Slope EXAMPLE SOLUTION SOLUTION Draw the graph of a function y = f ( T ) with the stated properties. Since f ( T ) is rising at an increasing rate , this means that the slope of the graph of f ( T ) will continually increase. The following is a possible example. In certain professions the average annual income has been rising at an increasing rate. Let f ( T ) denote the average annual income at year T for persons in one of these professions and sketch a graph that could represent f ( T ). 0 50 100 150 200 250 0 1 2 3 4 5 YEAR AVG ANNUAL INC Notice that the slope becomes continually steeper.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 10 of 107 Concavity Concave Up Concave Down
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 11 of 107 Inflection Points Notice that an inflection point is not where a graph changes from an increasing to a decreasing slope, but where the graph changes its concavity.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 12 of 107 Intercepts Definition Definition x-Intercept : A point at which a graph crosses the x -axis. y-Intercept : A point at which a graph crosses the y -axis.
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 13 of 107 Asymptotes Definition Definition Horizontal Asymptotes : A straight, horizontal line that a graph follows indefinitely as x increases without bound.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/04/2010 for the course MATH MATH 16B taught by Professor Unknown during the Spring '10 term at UC Davis.

Page1 / 107

Chapter2 - Chapter 2 Applications of the Derivative

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online