What is $F''(x)$ of function $F(x) = \max\limits_{c\in D}f(x,c)$?

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Let $D\subset \mathbb{R}$, and $f(x,c): \mathbb{R}\times \mathbb{R} \to \mathbb{R}$. What is $F''(x)$ of function $F(x) = \max\limits_{c\in D}f(x,c)$? Is it equal to $\max\limits_{c\in D}f''(x,c)$? Thank you in advace !