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I am interested in a relationship (if any) between the number of critical points of a periodic function $f$ of class $C^3([0,T])$ and the number of critical points of $f''$ in $[0,T]$.

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    What do you mean by "of class $C^3([0,T])$"? Do you mean that the periodic extension should also be three times continuously differentiable?2012-02-01
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    Yes, the periodic extension is of class $C^3$ on $\mathbb(R)$.2012-02-01

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