Bell RingerWhat are the points in which the f(x) has a horizontal tangent line? f(x) = 4x3 - 48x (2, -64) (2, 64) (2, -64) and (-2, 64) (2, 0) and (-2, 0) none of the above
Using the following position function, find the average velocity over the period of [1, 2]. s(t) = -16t2 + 100 -48 -40 -32 -30 none of the above
Using the function in #2, find the instantaneous velocity at t = 2. -64 -40 -32 -30 none of the above
Using the function in #2, find the instantaneous acceleration at t = 2. -64 -40 -32 -30 - 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
- Basic Differentiation Rules
- Constant Rule
- Power Rule
- Sum and Difference Rule
Lesson- Rates of Change
- Sine and Cosine Derivatives
- Practice (Section 2.2)
- Checkpoint #1
- Checkpoint #2
- Checkpoint #3
- Checkpoint #4
- 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:
- sine and cosine functions
- rates of change
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 |