Fermat's Theorem

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Calculus

Cegep/1

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56 words

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1 minute

If $f$ has a local extremum at $x = c$ , $f^{'} (c) = 0$ or undefined (i.e. local extremum $⟹$ [[critical point]]).

The inverse is only true if $f'$ changes sign across $x = c$.

Does not apply to global extrema which can occur at non critical points.

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