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. Monday, February 18, 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. Extrema (max) Inflection Point Inflection Point Inflection Point Extrema (min) Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 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. Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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. Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Monday, February 18, 2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals