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Soit \(f \in C^2 (\Rr)\) telle que \(\forall (x, y) \in \Rr^2 \, \, f (x + y)f (x-y) \leq f (x)^2\). Montrer que \(\forall x \in \Rr \, \, f (x)f'' (x) \leq f' (x)^2\).
Soit \(f \in C^2 (\Rr)\) telle que \(\forall (x, y) \in \Rr^2 \, \, f (x + y)f (x-y) \leq f (x)^2\). Montrer que \(\forall x \in \Rr \, \, f (x)f'' (x) \leq f' (x)^2\).