Update - Unit 3 Test on 3/27!
- If you are leaving for spring break early, please make arrangements with me to take the test before break!
Questions
Bell Ringer
Review
- Extrema/Critical Numbers (video)
- How is the derivative used to locate the minimum and maximum values of a function on a closed interval?
- Find critical numbers using differentiation.
- Find extrema on a closed interval using differentiation.
- Rolle's Theorem (video) and Mean Value Theorem (video)
- How are Rolle's Theorem and Mean Value Theorem related to differentiation?
- Apply understanding of Rolle’s Theorem and the Mean Value Theorem.
- Increasing/Decreasing Functions (video)
- How can the first derivative to determine whether a function is increasing or decreasing?
- Determine intervals on which a function is increasing or decreasing.
- Apply the First Derivative Test to find relative extrema of a function.
- Concavity and Inflection Points
- How can the second derivative be used to determine the concavity of intervals of a function? (video)
- Determine intervals on which a function in concave upward or downward.
- Apply the Second Derivative Test to find inflection points of a function.
- Limits at Infinity
- How can limits be used to find horizontal asymptotes of the graph of a function? (video)
- Determine horizontal asymptotes using limits.
- Determine finite limits at infinity.
- Determine infinite limits at infinity.
- Optimization
- How can differentiation be used to find optimal conditions of a scenario?
- Determine the conditions that optimize a situation.
Lesson
Exit Ticket
- Posted on the board at the end of the block
| Lesson Objective(s)
Skills
- Find critical numbers using differentiation.
- Find extrema on a closed interval using differentiation.
- Apply understanding of Rolle’s Theorem and the Mean Value Theorem.
- Determine intervals on which a function is increasing or decreasing.
- Apply the First Derivative Test to find relative extrema of a function.
- Determine intervals on which a function in concave upward or downward.
- Apply the Second Derivative Test to find inflection points of a function.
- Determine horizontal asymptotes using limits.
- Determine finite limits at infinity.
- Determine infinite limits at infinity.
- Determine the conditions that optimize a situation.
Standard(s)
- APC.4
- Investigate asymptotic and unbounded behavior in functions.
- Includes:
- describing and understanding asymptotes in terms of graphical behavior and limits involving infinity
- APC.8
- Apply the derivative to solve problems.
- Includes:
- analysis of curves and the ideas of concavity and monotonicity
- optimization involving global and local extrema
Past Checkpoints - Extrema/Critical Numbers
- Rolle's Theorem and Mean Value Theorem
- Increasing and Decreasing Functions
- Concavity and Inflection Points
- Extra Practice
- Limits at Infinity
- Extrema Example Problems
- Optimization
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