This document discusses key concepts related to finding local extrema and inflection points of functions including using the first and second derivatives to determine concavity, where local maxima and minima occur based on changes from increasing to decreasing or vice versa, and how inflection points involve a change in concavity. It also covers using critical numbers found by setting the derivative equal to zero to help identify local extrema and defines absolute extrema as the highest or lowest values over a given interval.

1. Local Max/Min

2. “Relative Extrema” M=0Local max – (increasing to decreasing)Local Min – (decreasing to increasing)First derivative

3. Concavity

4. Concave upConcave downSecond derivative

5. Inflection Points

6. Concave up to concave downConcave down to concave upChange in concavity

7. Critical Numbers

8. Set derivative equal to zero and solve for xCritical numbers that are undefined are not locals or inflection points

9. Absolute Max/Min

10. Absolute ExtremaTable of valuesMax: highest point in an intervalMin: lowest point in an interval