10230
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Fermat's Theorem on Stationary Points
Fermat's theorem on stationary points states that if
is a local extremum in the interval
and
is differentiable at
, then
.
Contributed by:
Julio Cesar de la Yncera
THINGS TO TRY
Slider Zoom
SNAPSHOTS
DETAILS
Snapshot 1: a local maximum; notice the slope is zero
Snapshot 2: a local minimum; the slope is also zero here; also notice the change of sign from positive to negative for the maximum and from negative slope to positive slope for the minimum
RELATED LINKS
Stationary Point
(
Wolfram
MathWorld
)
Extremum
(
Wolfram
MathWorld
)
Differentiable
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Fermat's Theorem on Stationary Points
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/FermatsTheoremOnStationaryPoints/
Contributed by:
Julio Cesar de la Yncera
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
Cauchy Mean-Value Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Bolzano's Theorem
Julio Cesar de la Yncera
Flett's Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Fundamental Theorem of Calculus
Chris Boucher
Slope between Two Points on a Curve
Trevor Cole
A Generalization of the Mean Value Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Marden's Theorem
Bruce Torrence
Lucas-Gauss Theorem
Bruce Torrence
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
Related Topics
Analysis
Calculus
Derivatives
High School Calculus and Analytic Geometry
High School Mathematics
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+