10044
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Cauchy Mean-Value Theorem
The Cauchy mean-value theorem states that if
and
are two functions continuous on
and differentiable on
, then there exists a point
in
such that
.
Geometric interpretation: Consider the parametric curve
,
,
; then the line passing through
,
is parallel to the tangent line passing through
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
THINGS TO TRY
Gamepad Controls
SNAPSHOTS
RELATED LINKS
Cauchy's Mean-Value Theorem
(
Wolfram
MathWorld
)
PERMANENT CITATION
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
"
Cauchy Mean-Value Theorem
"
http://demonstrations.wolfram.com/CauchyMeanValueTheorem/
Wolfram Demonstrations Project
Published: June 4, 2008
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
A Generalization of the Mean Value Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Flett's Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Mean Value Theorem
Michael Trott
Fermat's Theorem on Stationary Points
Julio Cesar de la Yncera
The Fundamental Theorem of Calculus
Chris Boucher
Squeeze Theorem
Bruce Atwood (Beloit College)
Two Integral Mean Value Theorems
Soledad María Sáez Martínez and Félix Martínez de la Rosa
Two Integral Mean Value Theorems of Flett Type
Soledad María Sáez Martínez and Félix Martínez de la Rosa
The Envelope Theorem: Numerical Examples
Jeff Hamrick
Bolzano's Theorem
Julio Cesar de la Yncera
Related Topics
Analysis
Calculus
College Mathematics
Derivatives
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+