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Satz 1: Das Vorzeichenwechsel-Kriterium für Extremstellen
Sei f eine differenzierbare Funktion deren Ableitung an der Stelle a eine Nullstelle hat

Damit ein lokales Maximum vorliegt, muss in der Ableitung f’ an der Stelle a ein Vorzeichenwechsel von + zu – erfolgen

Damit ein ein lokales Minimum vorliegt muss in der Ableitung f’ an der Stelle a ein Vorzeichenwechsel von – zu + erfolgen

Satz 2: Kriterium für Extremstellen mithilfe der zweiten Ableitung
Die Funktion f ist auf dem Intervall I zweimal differenzierbar und x0 eine innere Stelle von I

Wenn f'(x0)=0 und f”(x0)<0 gilt, dann hat die Funktion f an der Stelle x0 ein lokales Maximum

Wenn f'(x0)=0 und f”(x0)<0 gilt, dann hat die Funktion f an der Stelle x0 ein lokales Minimum


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