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Calculus 1
>
Lessons - Semester 2 (2014-2015)
>
Unit 3 - Applications of Differentiation
>
Day 46 - Optimization - 03.18.15
The gadget spec URL could not be found
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
Question Wall
Submit questions here!
Bell Ringer
Optimization
Optimization
Optimization
Optimization
Optimization
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.
Lesson
Optimization
Checkpoints
page 223
#17, 19, 25
Exit Ticket
Posted on the board at the end of the block
Lesson Objective(s)
How can differentiation be used to find optimal conditions of a scenario?
Skills
Determine the conditions that optimize a situation.
In-Class Help Requests
The gadget spec URL could not be found
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
Checkpoints
Rolle's Theorem and Mean Value Theorem
Checkpoints
Increasing and Decreasing Functions
Checkpoints
Concavity and Inflection Points
Checkpoints
Extra Practice
Absolute Extrema
Relative Extrema
Rolle's Theorem
Mean Value Theorem
Intervals of Increasing/Decreasing
Concavity
Limits at Infinity
Checkpoints
Extra Practice