1. Warm Up Cinco 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 Cinco
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2. inc dec inc f is decreasing f is increasing f is increasing max min
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.
There are two ways to test for relative extrema:
the 1st derivative test or the 2nd derivative test
f has a maximum
1st Derivative Test:
1.) Find Candidates
2.) Test for sign change in f’
3.) Verify continuity
Sign change in f’ Rel. extrema on f
if f is cont.
f is decreasing
f is increasing
f is increasing
inc
dec
inc
f has a minimum
max
min
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

3. inc dec inc 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.
There are two ways to test for relative extrema:
the 1st derivative test or the 2nd derivative test
1st Derivative Test:
1.) Find Candidates
2.) Test for sign change in f’
3.) Verify continuity
f has a max
Sign change in f’ Rel. extrema on f
if f is cont.
f has a min
inc
dec
inc
Max
min
Tuesday, April 09, 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.
2nd Derivative Test:
1.) Find Candidates
2.) Find sign of candidates in f”
3.) Verify continuity
Tuesday, April 09, 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.
2nd Derivative Test:
1.) Find Critical Values
2.) Find sign of C.V in f”
3.) Verify continuity
Tuesday, April 09, 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.
2nd Derivative Test:
1.) Find Critical Values
2.) Find sign of C.V in f”
3.) Verify continuity
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7. dec Inc 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.
Identify candidates by finding critical values.
x=1 is the only candidate to be an extrema but needs to be tested.
Find f”(x) and plug in x=1.
Plug in the 1st derivative to check for sign change
1st derivative Test
2nd derivative Test
dec
Inc
Make sure x=1 is continuous on f (not a vertical asymptote or removable discontinuity).
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8. dec Inc 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
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9. 2nd derivative test for extrema 1st derivative test for extrema
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.
2nd derivative test for extrema
1st derivative test for extrema
dec
Inc
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

10. 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 Pg. 189 #27-32, 35, 36 Use 1st Derivative test for extrema 4 times and 2nd derivative test for extrema 4 times,  45-48
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

11. 2nd derivative test for extrema
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.
2nd derivative test for extrema
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

12. 2nd derivative test for extrema
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.
2nd derivative test for extrema
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

13. 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.
Tuesday, April 09, 2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals