%0 Journal Article %A Ferrera Cuesta, Juan %T Norm-attaining polynomials and differentiability. %D 2002 %@ 0039-3223 %U https://hdl.handle.net/20.500.14352/57243 %X We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Frechet differentiable: We also characterize the Gateaux differentiability of the norm. Finally we study those properties for some classical Banach spaces. %~