From the course: Complete Guide to Calculus Foundations for Data Science
Join today to access over 24,800 courses taught by industry experts.
Intermediate value theorem
From the course: Complete Guide to Calculus Foundations for Data Science
Intermediate value theorem
- [Instructor] Let's wrap up this chapter with another theorem. In this video, I will show you the Intermediate Value Theorem and how to use it. Let's get started. The Intermediate Value Theorem states if a function f of x is continuous over a closed-bounded interval a to b and d is any number between f of a and f of b, then there exists a number c such that a less than c less than b and f of c equals d. Note that this theorem is sometimes shortened to just IVT. Let's look at this graphically to see the Intermediate Value Theorem in action. Let's look at the graph of this function, represented by the blue line, and this is a continuous function on this graph. Let's look at the values of x equals negative 2 and x equals 0. Since this function is continuous on a closed interval between negative 2 and 0, you can use the Intermediate Value Theorem to prove a root exists in that given interval. Using this theorem then guarantees that, if you check for a point, it will then have a…
Download courses and learn on the go
Watch courses on your mobile device without an internet connection. Download courses using your iOS or Android LinkedIn Learning app.