# 4.3 how dx affect shape of graph

### Card Set Information

 Author: jojobean0203 ID: 215009 Filename: 4.3 how dx affect shape of graph Updated: 2013-04-22 03:11:18 Tags: calc Folders: Description: how dx affect shape of graph Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user jojobean0203 on FreezingBlue Flashcards. What would you like to do?

1. inflection point
• any value of x where concavity changes
• more formally, point P on y = f(x) if f(x) is continuous @ that point if curve changes from CU to CD or from CD to CU @ P
2. increasing/decreasing test
• f'(x) is +: f(x) is increasing
• f'(x) is - : f(x) is decreasing
3. first dx test
• local max @ c: if f'(x) changes from + to - @ c
• local min @ c: if f'(x) changes from - to + @ c
• none @ c:  if f'(x) does not change sign @ c
4. concave upward
if graph of f(x) lies above all its tangents on an interval I
5. concave downward
if graph of f(x) lies below all its tangents on an interval I
6. second dx test helps determine
• * intervals of concavity
• * max & min values
7. concavity test
• concave up on I:  f"(x) + for all x in I
• concave down on I: f"(x) - for all x in I
8. second dx test
• f"(x) is continuous near c
• local max @ c: if f'(c) = 0 & f"(c) +
• local min @ c: if f'(c) = 0 & f"(c) -
9. inconclusive second dx test
• when f"(c) = 0 or when f"(c) dne
• max, min, or neither
10. T/F:
if f'(x) is increasing, f(x) is +
if f'(x) is decreasing, f(x) is -
F: inverse/backwards

• correct:
• if f(x) is increasing, f'(x) is +
• if f(x) is decreasing, f'(x) is -
11. T/F:
if f(x) is increasing, f'(x) is +
if f(x) is decreasing, f'(x) is -
T
12. What does f'(x) say about f(x)?
13. What does f"(x) say about f(x)?

What would you like to do?

Home > Flashcards > Print Preview