# Difference between revisions of "Intermediate Value Theorem"

(cat) |
m (→Statement) |
||

Line 2: | Line 2: | ||

==Statement== | ==Statement== | ||

− | Let <math>f:[a,b]\ | + | Let <math>f:[a,b]\rightarrow\mathbb{R}</math> |

Let <math>f</math> be continous on <math>[a,b]</math> | Let <math>f</math> be continous on <math>[a,b]</math> |

## Revision as of 20:01, 16 February 2008

The **Intermediate Value Theorem** is one of the very interesting properties of continous functions.

## Statement

Let

Let be continous on

Let

Then, such that

## Proof

Consider such that

note that and

By Location of roots theorem, such that

or

QED