  Consider the semilinear elliptic equation $-\Delta u=\lambda f(u)$ in the
unit ball $B_1\subset \mathbb{R}^N$, with Dirichlet data $u|_{\partial B_1}=0$,
where $\lambda\geq 0$ is a real parameter and $f$ is a $C^1$ positive,
nondecreasing and convex function in $[0,\infty)$ such that
$f(s)/s\rightarrow\infty$ as $s\rightarrow\infty$. In this paper we study the
behavior of $f'(u^\ast)$ near the origin when $u^\ast$, the extremal solution
of the previous problem associated to $\lambda=\lambda^\ast$, is singular. This
answers to an open problems posed by Brezis and V\'azquez.
