Fermat's Theorem on Stationary Points

value c

Fermat's theorem on stationary points states that if

c

is a local extremum in the interval

(a,b)

and

f

is differentiable at

c

, then

f'(c)=0

.

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

External Links

Stationary Point (Wolfram MathWorld)

Extremum (Wolfram MathWorld)

Differentiable (Wolfram MathWorld)

Permanent Citation

Julio Cesar de la Yncera

"Fermat's Theorem on Stationary Points"
http://demonstrations.wolfram.com/FermatsTheoremOnStationaryPoints/
Wolfram Demonstrations Project
Published: September 28, 2007