Join our community

Learn Morecaret down

caret down

Join our community

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students! ๐ŸŽ‰

group of students
group of students

ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

1.16 Working with the Intermediate Value Theorem (IVT)

#intermediatevaluetheorem

#ivt

โฑ๏ธย ย 1 min read

written by

Anusha Tekumulla

anusha tekumulla


The Intermediate Value Theorem (IVT)

The intermediate value theorem focuses on a crucial part of continuity: for any function f(x) that's continuous over the interval [a, b], the function will take any y-value between f(a) and f(b) over the interval.ย ๐Ÿ“ˆ

Specifically, it means that for any value L between f(a) and f(b), there's a value c in [a,b] for which f(c) = L.ย 

While this may sound confusing, it is actually very simple. As we have discussed before, continuous functions have to be drawn without lifting the pencil. If we know the graph passes through (a, f(a)) and (b, f(b)) then it must pass through any y-value between f(a) and f(b).

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fdownload.svg?alt=media&token=0c354704-9bca-401f-8cc4-204f59de4365

Image courtesy of Math is Fun

As you can see in the graph above, you can use the intermediate value theorem to prove that a function will cross a line at least once in an interval [a, b].ย ๐Ÿ‘

continue learning

Slide 1 of 17
Fiveable

Join Our Community

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

Fiveable Logo

2550 north lake drive
suite 2
milwaukee, wi 53211

92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2020 | all rights reserved.