  Let $f:I \to I$ be a $C^2$ multimodal interval map satisfying polynomial
growth of the derivatives along critical orbits. We prove the existence and
uniqueness of equilibrium states for the potential $\phi_t:x\mapsto
-t\log|Df(x)|$ for $t$ close to 1, and also that the pressure function $t
\mapsto P(\phi_t)$ is analytic on an appropriate interval near $t = 1$.
