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May 10 at 14:57 vote accept Doofenshmert
May 10 at 12:20 answer added Iosif Pinelis timeline score: 1
May 10 at 12:03 comment added Fedor Petrov Claim seems to be very much false, even if $n=1$ and $f$ is a polynomial. Choose, say, $a=0.9$, $y=a$, $x=a/2$, $f(x)=9,f(y)=11$. There is a smooth increasing function with such values, with positive derivative. Approximate its derivative by a polynomial by Weierstrass theorem, and take antiderivative of this polynomial
May 10 at 11:19 history asked Doofenshmert CC BY-SA 4.0