### Day 17 - Basic Differentiation Rules - 09.10.14

Bell Ringer
1. Find f(x + h), if f(x) = x3

1. x3 + 2hx2 + 2h2x + xh2 + h3

2. x3 + 3hx2 + 3h2x + h3

3. x3 + hx2 + 2h2x + xh2 + h3

4. x3 + hx2 + 2hx2 +2h2x + xh2

5. none of the above

2. Find the derivative of the following function: f(x) = x3 + 2x

1. 3x2 + 2

2. 3x2 - 2

3. 3x2

4. -3x2 + 2

5. none of the above

3. Find the slope of the tangent line at (1, 1) of the following function: f(x) = x1/2

1. 1 / (2x1/2)

2. 1 / 2

3. -1 / 2

4. 2x1/2

5. none of the above

4. Find f’(t) and f’(3) based on f(t) = 2 / t

1. f’(t) = 2 / t2 and f’(3) = 2 / 9

2. f’(t) = -2 / t2 and f’(3) = 2 / 9

3. f’(t) = -2 / t2 and f’(3) = -2 / 9

4. f’(t) = 2 / t2 and f’(3) = -2 / 9

5. none of the above

5. What are the points in which the f(x) has a horizontal tangent line? f(x) = x3 - 3x

1. (1, 2)

2. (-1, 2)

3. (0, 0)

4. (1, -1)

5. none of the above

Review
• Secant vs. Tangent Line
• Slope
• Definition of Derivative
• Importance of Derivative
• What does it allow us to do?
• Drawing a Tangent Line on a Graph

Lesson
• Basic Differentiation Rules
• Constant Rule
• Power Rule
• Sum and Difference Rule
• Practice
• page 115 #1
• Checkpoint #1
• page 115 #2
• page 115 #3-17 (odds)
• Checkpoint #2
• page 115 #10
• Checkpoint #3
• page 115 #18
• page 115 #39-49 (odds)
• Checkpoint #4
• page 115 #50
• Checkpoint #5
• page 115 #52
• page 116 #59 and 61
• Checkpoint #6
• page 116 #62
• Work on Student-led Lessons!

Exit Ticket
• Exit TIcket will be posted on the board in class.
Lesson Objective(s)
• What rules can be created for finding the derivative involving:
• constants
• powers
• sum and differences

Standard(s)
• APC.5
• Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.
• The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.
• APC.6
• ​The student will investigate the derivative at a point on a curve.
• Includes:
• finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangents
• using local linear approximation to find the slope of a tangent line to a curve at the point
• ​defining instantaneous rate of change as the limit of average rate of change
• approximating rate of change from graphs and tables of values.

Mathematical Practice(s)
• #1 - Make sense of problems and persevere in solving them
• #2 - Reason abstractly and quantitatively
• #3 - Construct viable arguments and critique the reasoning of others
• #4 - Model with mathematics
• #8 - Look for and express regularity in repeated reasoning