Solution
= Solution
On $b=-\eta a$ with $a>0$,
$$
\frac{db}{da}=\frac{-cb-f(a)}b=-c+\frac{f(a)}{\eta a}
=-c+\frac{\eta^2-a^2}{\eta(1+a^2)}\leq-c+\eta<-\eta.
$$
Thus $\boxed{db/da<-\eta}$. Since $a'=b<0$, comparing slopes alone can reverse one's intuition about crossing direction. More directly, for $H=b+\eta a$ the inward test is
$$
H'=b'+\eta a'=\eta(c-\eta)a-f(a)\geq\eta(c-2\eta)a>0,
$$
so the sloping edge also points into $H\geq0$.