1. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Extrema (max)
Inflection Point
Inflection Point
Inflection Point
Extrema (min)
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

3. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

4. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

5. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

6. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

10. CU CD Chapter 3.4 Concavity and the Second Derivative Test f”
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing. CU CD f”
+ (positive)
- (negative) f’
Increasing
decreasing f
Concave up
Concave down
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

11. CU CD CU Chapter 3.4 Concavity and the Second Derivative Test f”
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing. CU CD CU f”
+ (positive)
- (negative) f’
Increasing
decreasing f
Concave up
Concave down
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

12. dec inc dec CD CU CD Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
dec
inc
dec CD CU CD f”
+ (positive)
- (negative) f’
Increasing
decreasing f
Concave up
Concave down
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

13. dec inc CU CD Chapter 3.4 Concavity and the Second Derivative Test f”
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
inc
dec CU CD f”
+ (positive)
- (negative) f’
Increasing
decreasing f
Concave up
Concave down
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

14. dec inc dec CD CU CD Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
dec
inc
dec CD CU CD f”
+ (positive)
- (negative) f’
Increasing
decreasing f
Concave up
Concave down
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

15. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

16. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

17. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

18. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

19. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

20. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

21. Concavity and the Second Derivative Test
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

22. This is how the signs of f, f’ , and f” affect the graph of f.
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
This is how the signs of f, f’ , and f” affect the graph of f.
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

23. 2nd Derivative Graphs Worksheet
Chapter 3.4
Concavity and the Second Derivative Test
4.3 Students understand the relation between differentiability and continuity.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Practice:
2nd Derivative Graphs Worksheet
Thursday, February 28, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals