= Solution
At the leading edge $b\to0$ and $g\to1$. The linearized <bacterial> equation is
$$
b''+cb'+b=0,
$$
with <characteristic exponents>
$$
\lambda_\pm=\frac{-c\pm\sqrt{c^2-4}}2.
$$
For $0<c<2$ they form a <nonreal> <complex conjugate> pair. A nonzero profile approaching the <travelling front> then has an exponentially decaying oscillatory leading term, and repeatedly changes sign. This is incompatible with the assumed positive <bacterial density>. The leading edge must therefore have real <characteristic exponents>, requiring
$$
\boxed{c\ge2.}
$$
At $c=2$ the repeated <characteristic exponent> is $-1$ and <polynomial> factors in the asymptotic profile may occur. The argument supplies a necessary lower bound; it is not an independent existence proof for every speed satisfying it.
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