Is it possible to find a differentiable $f:\mathbb{R} \rightarrow \mathbb{R}$ such that
$ xf(x) \geq L \quad \forall x \in \mathbb{R} $
for an arbitrary constant $L>0$ ?
Is it possible to find a differentiable $f:\mathbb{R} \rightarrow \mathbb{R}$ such that
$ xf(x) \geq L \quad \forall x \in \mathbb{R} $
for an arbitrary constant $L>0$ ?
Hint. See what happens for $x = 0$.
At every other point $f(x) = L/x$ would work.