Conserved Quantities in $f(R)$ Gravity via Noether Symmetry

This paper is devoted to investigate $f(R)$ gravity using Noether symmetry approach. For this purpose, we consider Friedmann Robertson-Walker (FRW) universe and spherically symmetric spacetimes. The Noether symmetry generators are evaluated for some specific choice of $f(R)$ models in the presence of gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.