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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
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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
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