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.
Lesson Extrema Example Problems
 Optimization
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.
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
