Wize University Calculus 1 Textbook > Applications of Differentiation

Fermat's Theorem

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Fermat's Theorem
Let f(x)f(x)f(x)be a real valued function on the interval (a,b)\left(a,b\right)(a,b) and suppose a<c<ba<c<ba<c<b where f(c)f(c)f(c)is a local extremum. If f(x)f(x)f(x) is differentiable at ccc then 

f′(c)=0\boxed{f'(c)=0}f′(c)=0​
  

Extra Practice

Fermat's theorem

Practice
True of False? If (c,f(c))\left(c,f\left(c\right)\right)(c,f(c)) is a maximum, then we must have that f′(c)=0f'\left(c\right)=0f′(c)=0.