Inegalitate diferentiala
Posted: Sat Oct 11, 2008 6:22 pm
Fie \( f:\mathbb{R}\to\mathbb{R} \) o functie de doua ori derivabila pe \( \mathbb{R} \) cu derivata a doua continua astfel incat \( f(x+y)\cdot f(x-y)\leq f^{2}(x), \forall x, y\in\mathbb{R} \). Aratati ca
\( f(x)\cdot f^{{\prime}{\prime}}(x)\leq (f^{\prime}(x))^{2}, \forall x \in\mathbb{R} \).
Gazeta Matematica, seria B 2001
\( f(x)\cdot f^{{\prime}{\prime}}(x)\leq (f^{\prime}(x))^{2}, \forall x \in\mathbb{R} \).
Gazeta Matematica, seria B 2001