PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
Rolle's theorem (Theorem)

Rolle's theorem. If $f$ is a continuous function on $[a,b]$, such that $f(a)=f(b)$ and differentiable on $(a,b)$ then there exists a point $c\in(a,b)$ such that $f'(c)=0$.

\includegraphics{rolle}



"Rolle's theorem" is owned by drini. [ owner history (1) ]
(view preamble)

View style:

See Also: intermediate value theorem, mean-value theorem


Attachments:
proof of Rolle's theorem (Proof) by rmilson
Log in to rate this entry.
(view current ratings)

Cross-references: point, differentiable, continuous function
There are 5 references to this entry.

This is version 9 of Rolle's theorem, born on 2001-10-20, modified 2005-03-06.
Object id is 422, canonical name is RollesTheorem.
Accessed 8941 times total.

Classification:
AMS MSC26A06 (Real functions :: Functions of one variable :: One-variable calculus)

Pending Errata and Addenda
None.
[ View all 5 ]
Discussion
Style: Expand: Order:
forum policy
zero by vitriol on 2002-02-21 16:06:49
a and b can also be both zero, is what i meant in my correction
[ reply | up ]

Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)