= Solution
Assume $c\leq0$, bounded coefficients and uniform ellipticity near the boundary point, an interior tangent ball there, and enough regularity for the boundary normal derivative. The <Hopf boundary point lemma> says that a nonnegative maximum at $x_0$ with strictly smaller values inside the tangent ball satisfies
$$
\boxed{\partial_\nu v(x_0)>0}
$$
for the outward unit normal. If $c=0$, the maximum can have either sign. Without existence of a classical derivative, one states a strict one-sided derivative bound.
The PDF also asks to deduce the <strong maximum principle for elliptic operators>; that request is missing from the TeX transcription. Suppose $v$ attains a nonnegative global maximum $M$ inside a connected domain but is not constant. A ball in $\{v<M\}$ can be chosen relatively compact in the domain and tangent to $\{v=M\}$ at an interior point $z$: use the distance from a nearby point to the closed maximum set. The <Hopf boundary point lemma> on that ball gives a nonzero outward derivative at $z$, contradicting $Dv(z)=0$ at an interior maximum. Therefore $v$ is constant. When $c=0$, the same proof works for a maximum of either sign.
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