If $f(x)$ is strictly convex, and
$\lim_{x\to \infty}\left(f(x) - x - ue^{x}\right) = w$
for some $u\ge 0$ and $w$ then what can be said about:
$g(x) = ve^{-x} + f(x)$
on $x\ge0$ where $v$ is some fixed real number. Can I say that it has exactly one minimum?