5.1 Extrema on an Interval.pptx - MATH 12 5.1 Extrema on an Interval What are \u2018extrema\u2019 Lesson Objective By the end of the lesson I will be able

5.1 Extrema on an Interval.pptx - MATH 12 5.1 Extrema on an...

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5.1 Extrema on an Interval What are ‘extrema’? 10/29/19 MATH 12
Lesson Objective By the end of the lesson, I will be able to… To learn to find the critical numbers of a function and to find the maximum and minimum values of a function.
Maximums and Minimums Absolute maximum The highest point on the graph is the absolute maximum if for all in Absolute minimum The lowest point on the graph is the absolute minimum if for all in
Maximums and Minimums Relative maximum The highest point on the graph compared to neighboring domain Relative minimum The lowest point on the graph compared to neighboring domain
Ex1. Using your graphing calculator…Identify any absolute and local maxima and minima for: for .
Critical numbers and Critical Points
Critical numbers and Critical Points A critical point is a point on the graph of where or . A critical number is a number in the domain of such that or .
Ex2. Find the Critical Numbers of: a) b) c)
Finding Absolute extrema algebraicallyTo find the extrema of a continuous function on a closed interval …1)Find ; determine the critical numbers, 2)Evaluate for all 3)Evaluate your end points: and 4)Compare values from step 2 and 3 to determine extremaF(a) must be a … because compared to …, it is …
Ex3. Find all extrema in the following functionsa) , on the interval b) on the interval ]F(a) must be a … because compared to …, it is …
Lesson Objective By the end of the lesson, I will be able to… To learn to find the critical numbers of a function and to find the maximum and minimum values of a function.
Suggested Practice Page 329 #1-25, 47-51, 59, 61 (Do only odd numbers.) Vocabulary: Absolute extrema, absolute maximum/minimum, relative (local) maximum/minimum, critical point, critical number.

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