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Preview
Derivatives came in very handy in single-variable calculus when trying to maximize or minimize a function. In this lesson we'll explore optimization theory in the multivariable context.
In Module 1 we'll discuss local extrema. We'll see that much of the terminology we're used to--like "critical points"--and how we used them to find local extrema carry over into the multivariable context.
Finally, in Module 2 we'll discuss absolute extrema. Here the situation will be more complicated than in single-variable calculus, because the "endpoints" of the domain we extremize over will become a two-dimensional boundary. Nevertheless, the procedure for finding the absolute extrema of multivariable functions we'll develop will be very similar to the one you remember from single-variable calculus.
Review
Review
Learn
Learn
Work through the lesson notes below, consulting the videos below it when you get to the "See Class Notes" boxes. For your records, the annotated lesson notes are below the videos. Some tips for you as you work through these resources:
I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.
Lesson Notes
Lesson Notes
Lesson 8.pdfModule 1 Video
Module 1 Video
Module 2 Video
Module 2 Video
Reflect
Reflect
If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:
Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.
Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.
If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:
Please summarize the main mathematical takeaways from the lesson notes.
What was the most interesting part of what you learned, and why?
What, if anything, do you still find confusing?
Practice
Practice
Work through the practice problems suggested below to see how much of this lesson you've understood.
Lesson 8 PP.pdfPage updated
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