1. Warm Up 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.
Warm Up
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2. Warm Up 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.
Warm Up
Wednesday, July 24, 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.
Inflection
Point
Inflection
Point
Inflection
Point
Inflection
Point
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

4. Extrema require continuity of f and a sign change in 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.
Extrema require continuity of f and a sign change in f’
Inflection points require continuity of f and a sign change in f’’
Critical values are “candidates” to become extrema. Not all critical values are extrema, but all extrema are critical values.
____________are “candidates” to become inflection points. Not all __________are inflection points, but all inflection points are _____________
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

5. C.D. C.U. 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.
Plug numbers into f” to determine concavity of f
C.D.
C.U.
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

6. 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.
C.D.
C.U.
C.D.
C.U.
Plug numbers into f” to determine concavity of f
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7. C.U. No inflection points. 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.
Outside the domain of f
C.U.
No inflection points.
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8. C.U. 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.
C.U.
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9. Practice: 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:
Wednesday, July 24, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals