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 Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 Thursday, November 29, 2018 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. Inflection Point Inflection Point Inflection Point Inflection Point Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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 _____________ Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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. Thursday, November 29, 2018 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. C.D. C.U. C.D. C.U. Plug numbers into f” to determine concavity of f Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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. Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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. Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

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: Thursday, November 29, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals