  Let $f_t:[0,1] \to [0,1]$ be a family of piecewise expanding unimodal maps
with a common critical point that is dense for almost all $t \in [a,b]$. If
$\mu_t$ is the corresponding SRB measure for $f_t$, we study the regularity of
$\Gamma(t)=\int \phi d\mu_t$ when assuming that the family is transversal to
the topological classes of these maps, more precisely, we prove that if
$J_t(c)=\sum_{k=0}^{\infty} \frac{v_t(f_t^k(c))}{Df_t^k(f_t(c))} \neq 0$ for
all $t$, where $v_t(x)=\partial_s f_s(x)|_{s=t}$, then $\Gamma(t)$ is not
Lipschitz for almost all $t\in [a,b]$. Furthermore, we give the exact modulus
of continuity of $\Gamma(t)$.
