1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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