  It is well known that a family of tent-like maps with bounded derivatives has
no linear response for typical deterministic perturbations changing the value
of the turning point. In this note we prove the following result: if we
consider a tent-like family with a \emph{cusp} at the turning point, we recover
the linear response.
  More precisely, let $T_\eps$ be a family of such cusp maps generated by
changing the value of the turning point of $T_0$ by a deterministic
perturbation and let $h_\eps$ be the corresponding invariant density. We prove
that $\eps\mapsto h_\eps$ is differentiable in $L^1$ and provide a formula for
its derivative.
