MathDB
KöMaL A. 723

Source: KöMaL A. 723

May 12, 2018
real analysiscollege contests

Problem Statement

Let f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} be a continuous function such that the limit g(x)=lim⁡h→0f(x+h)−2f(x)+f(x−h)h2g(x)=\lim_{h\rightarrow 0}{\frac{f(x+h)-2f(x)+f(x-h)}{h^2}} exists for all real xx. Prove that g(x)g(x) is constant if and only if f(x)f(x) is a polynomial function whose degree is at most 22.
Back to ProblemsView on AoPS