# Polynomfunktion/Funktionsverlauf aus Differenzierbarkeit/Fakt/Beweis/Aufgabe/en

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Prove that a real polynomial function

${\displaystyle f\colon \mathbb {R} \longrightarrow \mathbb {R} }$

of degree ${\displaystyle {}d\geq 1}$ has at most ${\displaystyle {}d-1}$ extrema, and moreover the real numbers can be divided into at most ${\displaystyle {}d}$ sections, where ${\displaystyle {}f}$ is strictly increasing or strictly decreasing.