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AP Calculus AB

AP Calculus AB. Free Response Question 2008 #6. The Question. Graphs of f and f’. Graph of f. Graph of f’. 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:. Part A (cont’d). Point:.

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AP Calculus AB

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  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

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