Calculus Review Maximum and Minimum Values of Functions
In this video we talk all about maximums and minimums (absolute/global and relative/local) and how you'll want to go about using calculus to justify them. This is intended as a review for AP Calculus students prepping for the AP Calculus AB and BC exams but will be useful to any calculus student. We go over what it means to be an absolute vs. local max or min; the first derivative test; the second derivative test; when to use which; the Candidates Test; the Extreme Value Theorem (EVT); the "Lonely Critical Point Theorem"; finding the range of a function using maximums, minimums, and limits at infinity; a giant list of all the parts of all the FRQs that these have shown up on since 1998. (I made the video in dark mode since that seems pretty popular!)
00:00 Relative vs Absolute Max/min
01:40 Things to know about relative maximums and minimums
04:00 First Derivative Test for Relative Max/Min
07:58 Second Derivative Test for Relative Max/Min
10:59 When to use which test?
14:25 Things to know about absolute maximums and minimums
17:02 The Candidates Test
20:57 The Extreme Value Theorem
22:51 The Lonely Critical Point Theorem
26:11 Finding the range of a function
29:17 List of every FRQ part that contains these ideas since 1998