# The Theorems of Differential Calculus

- Author:
- Charlie Barnes, Tim Brzezinski

- Topic:
- Calculus, Differential Calculus

Below are statements of theorems from differential calculus with accompanying visualizations.

## The Squeeze Theorem

If:
.

, , and are all continuous functions over , -
, is between and on , and ,

## The Intermediate Value Theorem

If:
in such that .

is continuous over and is a number between and

## The Extreme Value Theorem

If:
and in such that for every in and for every in .

is continuous over ,

## The Mean Value Theorem

If:
such that .

is continuous over and is differentiable over ,

## L'Hopital's Rule

If:
.

and are both differentiable near , or , and exists,