here is the problem:(adsbygoogle = window.adsbygoogle || []).push({});

we know that

(1) f(x) is defined on [tex](-\infty, +\infty)[/tex], and f(x) has the second derivative everywhere,

(2) [tex]lim_{|x|\rightarrow+\infty}(f(x)-|x|)=0[/tex],

(3) there is [tex]x_0\in R[/tex] such that [tex]f(x_0)\leq0[/tex]

how do we prove that f"(x) changes sign on [tex](-\infty, +\infty)[/tex]?

I can imagine that the graph of f(x) can't be always convex or concave on the real line, but how do I put it in hard argument?

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# Convexity and concavity of a function

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