Bell RingerFind f(x + h), if f(x) = x3 x3 + 2hx2 + 2h2x + xh2 + h3 x3 + 3hx2 + 3h2x + h3 x3 + hx2 + 2h2x + xh2 + h3 x3 + hx2 + 2hx2 +2h2x + xh2 none of the above
Find the derivative of the following function: f(x) = x3 + 2x 3x2 + 2 3x2 - 2 3x2 -3x2 + 2 none of the above
Find the slope of the tangent line at (1, 1) of the following function: f(x) = x1/2 1 / (2x1/2) 1 / 2 -1 / 2 2x1/2 none of the above
Find f’(t) and f’(3) based on f(t) = 2 / t f’(t) = 2 / t2 and f’(3) = 2 / 9 f’(t) = -2 / t2 and f’(3) = 2 / 9 f’(t) = -2 / t2 and f’(3) = -2 / 9 f’(t) = 2 / t2 and f’(3) = -2 / 9 none of the above
What are the points in which the f(x) has a horizontal tangent line? f(x) = x3 - 3x (1, 2) (-1, 2) (0, 0) (1, -1) - none of the above
Review- Secant vs. Tangent Line
- 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 #3-17 (odds)
- Checkpoint #2
- Checkpoint #3
- page 115 #39-49 (odds)
- Checkpoint #4
- Checkpoint #5
- page 116 #59 and 61
- Checkpoint #6
- 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
In-class Help RequestIn-class Help Request |