We can interpret the trace of the field equations as a motion equation for f' (R). Also we should parameterize the deviation from Einstein gravity as $f(R)=R+\epsilon * \phi(R) $. where $\epsilon$ is a small parameter (~$H_{0}^{2}=(10^{-66})(eV)^{2}$). By substituting this f(R) in the trace of field eqs. and to first order $\epsilon$, we obtain a reduced motion equation. Here it's necessary to consider a small region of space-time in the weak field regime, in which curvature and metric are $R=\kappa^{2} T +R_{1}$ and $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$. where $R_{1}$ is curvature perturbation and $h_{\mu\nu}$ is the perturbation in Minkowski metric. The substitute of these relations lead us to a second order differential equation for $R_{1}$, where coefficient of $R_{1}$ determines the existence of tachyon-like instability. Since this coefficient play the role of the square of the effective mass. The positivity of this term avoids a tachyon-like instability. In the f(R) gravity this term related to f''(R).