Extrema on an Interval | Calculus Lesson 19 – JK Math

How to find Extrema on an Interval (Calculus Lesson 19)

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In this lesson we learn how to find extrema on an interval. We start by defining extrema and the 4 different types of extrema. These are absolute maximums and minimums, and relative maximums and minimums. We learn how to locate these types of extrema visually on a graph, and then move into how to find absolute extrema for a function on an interval without a graph (analytically). We briefly discuss the extreme value theorem, and how relative extrema can be found at points on a function where the slope is 0 or does not exist. We go over the basic guidelines/steps to finding absolute extrema analytically and then look at one example using those steps.

This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes!

Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 What are Extrema?
1:25 Locating Absolute and Relative Extrema on a Graph
3:38 Why Extrema on an Interval?
5:25 The Extreme Value Theorem
6:00 The Slope at Extrema & Critical Numbers
8:15 Guidelines for Finding Extrema on a Closed Interval
9:25 Example – Finding Absolute Extrema for -x^2+3x on [0,3]

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#calculus

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