Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.5: Adjectives for Functions"

Read Section 2.5 (pages 51-54). The intuitive notion of a continuous function is made precise using limits. In addition, you will be introduced to the Intermediate Value Theorem, which rigorously captures the intuitive behavior of continuous real-valued functions.

Click https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/07/calculus_02_Instantaneous_Rate_of_Change-_The_Derivative.pdf link to open resource.