Course: Calculus I
Topic: Analysis of Curves
Subtopic: Extreme Values


Graphs of functions have several important points such as the "bottom of a valley" or a "sharp corner". These points can be found using information obtained from the tangent line (derivative) to the graph. Points such as those occurring at the "top of a hill" are particularly useful for optimizing a function, such as finding the largest "extreme" point through which it can pass. We begin our study of important "critical" points and the analysis of curves in this lesson.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: horizontal tangent line, vertical tangent line, sharp corner, cusp, critical point, critical value, relative extreme point, relative minimum point, relative maximum point, relative extrema, relative extrema theorem, absolute extrema

Mini-Lectures and Examples

STUDY: Analysis of Curves - Extrema, CPs, MVT

Supplementary Resources (optional)

Video: Extreme Values on Intervals, Selwyn Hollis's Video Calculus

Lesson: Finding Maximums and Minimums, Dale Hoffman's Contemporary Calculus

rev. 2020-10-31