dana-mccall
Uploaded by
12 SLIDES
254 VUES
120LIKES

Understanding Graphs of Functions and Derivatives in AP Calculus AB: Free Response 2008 Question 6

DESCRIPTION

This resource provides a detailed breakdown of AP Calculus AB Free Response Question 6 from 2008, which explores the key concepts of tangent lines, critical points, relative extrema, points of inflection, and limits. Part A guides students through deriving the equation of a tangent line using the point-slope formula. Part B discusses how to find critical points and use the first derivative test to determine their nature. Part C identifies points of inflection by analyzing the second derivative, while Part D elaborates on ways to evaluate limits. Ideal for AP Calculus exam preparation.

1 / 12

Télécharger la présentation

Understanding Graphs of Functions and Derivatives in AP Calculus AB: Free Response 2008 Question 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. AP Calculus AB Free Response Question 2008 #6

  2. The Question

  3. Graphs of f and f’ Graph of f Graph of f’

  4. Part A • Write an equation for the line tangent to • To write an equation, we need to find the point and the slope of the specific x Point: Slope:

  5. Part A (cont’d) Point: Slope: • After we obtained the slope and the point, we can apply them to point-slope formula to write an equation Point-Slope Formula:

  6. Part B • Find the x-coordinate of the critical point of . Determine whether this point is a relative minimum, a relative maximum, or neither for the function . Justify your answer. • To find critical point, we set first derivative to zero.

  7. Part B (cont’d) • After we found the critical point, we can determine its relative condition by the 1st derivative test. Since the f’(x) changes from positive to negative, f (x) obtains relative maximum at x=e.

  8. Part C • The graph of the function has exactly one point of inflection. Find the x-coordinate of this point. • Point of inflection: point where changes of concavity happened We can find point of inflection by setting 2nd derivative to zero. Since = 0 at , the x-coordinate of the point of inflection is

  9. Part D Find • There are three ways to find a limit. • Numerically • Directly plug in number into the original function

  10. Part D (cont’d) • 2.Graphically As the graph clearly shown, when x approaches to 0 from the right, the function gets closer to .

  11. Part D (cont’d) • 3. Analysis As the value of x get closer and closer to 0, the y value graduate get closer and closer to negative infinite

  12. THANK YOU

More Related