  We study the stability of f(R)-AdS (Schwarzschild-AdS) black hole obtained
from f(R) gravity. In order to resolve the difficulty of solving fourth order
linearized equations, we transform f(R) gravity into the scalar-tensor theory
by introducing two auxiliary scalars. In this case, the linearized curvature
scalar becomes a dynamical scalaron, showing that all linearized equations are
second order. Using the positivity of gravitational potentials and S-deformed
technique allows us to guarantee the stability of f(R)-AdS black hole if the
scalaron mass squared satisfies the Breitenlohner-Freedman bound. This is
confirmed by computing quasinormal frequencies of the scalaron for large
f(R)-AdS black hole.
