Chapter 3.3 Increasing and Decreasing Functions and the first 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 Draw the graph of 1 function with all of the following characteristics: Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Non Removable discontinuity Chapter 3.3 Increasing and Decreasing Functions and the first 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. positive decreasing Non Removable discontinuity increasing negative Minimum (sharp turn) dec inc 1 x -3 -2 -1 1 2 3 4 5 f ‘(x) x -3 -2 -1 1 2 3 4 5 f ‘(x) DNE x -3 -2 -1 1 2 3 4 5 f ‘(x) x -3 -2 -1 1 2 3 4 5 f ‘(x) Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Non Removable discontinuity Chapter 3.3 Increasing and Decreasing Functions and the first 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. Maximum (sharp turn) positive decreasing increasing Non Removable discontinuity negative x -2 -1 1 2 f ‘(x) x -2 -1 1 2 f ‘(x) DNE inc dec Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. increasing positive decreasing x-intercept negative minimum (smooth turn) x -6 -4 -2 2 f ‘(x) -1 x -6 -4 -2 2 f ‘(x) -1 x -6 -4 -2 2 f ‘(x) x -6 -4 -2 2 f ‘(x) x -6 -4 -2 2 f ‘(x) -1 1 x -6 -4 -2 2 f ‘(x) -1 1 dec inc -2 Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. maximum (smooth turn) positive x-intercept increasing decreasing negative x 2 3 4 5 6 f ‘(x) x 2 3 4 5 6 f ‘(x) -2 -4 inc dec 4 Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. Inc Dec max Dec Inc min Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Practice: Derivative Graphs Worksheet Chapter 3.3 Increasing and Decreasing Functions and the first 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: Derivative Graphs Worksheet Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 3.3 Increasing and Decreasing Functions and the first 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. Wednesday, October 8, 2014 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals