Lesson 10: What does f' say about f?

1,788 views

Published on

This isn't very complete but it does give the highlights of the section.

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,788
On SlideShare
0
From Embeds
0
Number of Embeds
34
Actions
Shares
0
Downloads
26
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Lesson 10: What does f' say about f?

  1. 1. Section 2.9 What does f say about f ? Math 1a October 17, 2007 Announcements Midterm I review session 10/21, 7:30pm in Hall D?
  2. 2. Outline Increasing and Decreasing functions Concavity and the second derivative
  3. 3. Definition Let f be a function defined on and interval I . f is called increasing if f (x1 ) < f (x2 ) whenever x1 < x2 for all x1 and x2 in I .
  4. 4. Definition Let f be a function defined on and interval I . f is called increasing if f (x1 ) < f (x2 ) whenever x1 < x2 for all x1 and x2 in I . f is called decreasing if f (x1 ) > f (x2 ) whenever x1 < x2 for all x1 and x2 in I .
  5. 5. Fact If f is increasing on (a, b), then f (x) ≥ 0 for all x in (a, b)
  6. 6. Fact If f is increasing on (a, b), then f (x) ≥ 0 for all x in (a, b) If f is decreasing on (a, b), then f (x) ≤ 0 for all x in (a, b).
  7. 7. Fact If f (x) > 0 for all x in (a, b), then f is increasing on (a, b). If f (x) < 0 for all x in (a, b), then f is decreasing on (a, b).
  8. 8. Outline Increasing and Decreasing functions Concavity and the second derivative
  9. 9. Definition A function is called concave up on an interval if f is increasing on that interval.
  10. 10. Definition A function is called concave up on an interval if f is increasing on that interval. A function is called concave down on an interval if f is decreasing on that interval.
  11. 11. Fact If f is concave up on (a, b), then f (x) ≥ 0 for all x in (a, b)
  12. 12. Fact If f is concave up on (a, b), then f (x) ≥ 0 for all x in (a, b) If f is concave down on (a, b), then f (x) ≤ 0 for all x in (a, b).
  13. 13. Fact If f (x) > 0 for all x in (a, b), then f is concave up on (a, b). If f (x) < 0 for all x in (a, b), then f is concave down on (a, b).

×