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

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

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

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

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

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

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

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

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

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

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

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

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