# The Theorems of 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
• ,
then .

## The Intermediate Value Theorem

If:
• is continuous over and
• is a number between and
then there is a number in such that .

## The Extreme Value Theorem

If:
• is continuous over ,
then there are numbers and in such that for every in and for every in .

## The Mean Value Theorem

If:
• is continuous over and
• is differentiable over ,
then there is a number such that .

## L'Hopital's Rule

If:
• and are both differentiable near ,
• or , and
• exists,
then .