© 2019
Der Funktionswert f(x0) heißt lokales Maximum von f bzw. lokales Minimum von f, wenn es eine Umgebung U von x0 gibt, sodass für alle Werte ∈ U gilt
f(x) ≤ f(x0) bzw. f(x) ≥ f(x0)
Satz: Sei f auf einem Intervall I differenzierbar und x0 ∈ I.
Wenn f an der Stelle x0 einen Extrempunkt besitzt, so gilt: f'(x0)=0
Daraus folgt:
Jede Extremstelle von f muss eine Nullstelle von f’ sein
Die Umkehrung gilt nicht.
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