The Ext-algebra for infinitesimal deformations

Let $f$ be a Hochschild $2$-cocycle and let $A_f$ be an infinitesimal deformation of an associative finite dimensional algebra $A$ over an algebraically closed field $\mathbb{k}$. We investigate the algebra structure of the Ext-algebra of $A_f$ and, under some conditions on $f$, we describe it in terms of the Ext-algebra of $A$. We achieve this description by getting an explicit construction of minimal projective resolutions in $\mathrm{m}\mathrm{o}\mathrm{d}{A}_f$.