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 $[0,T]$.
Number of critical points in a period of a periodic function
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calculus
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1What 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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0Yes, the periodic extension is of class $C^3$ on $\mathbb(R)$. – 2012-02-01