Let A be an augmented algebra over a semi-simple algebra S. We
show that the Ext algebra of S as an A-module, enriched with its natural
A-infinity structure, can be used to reconstruct the completion of A at the
augmentation ideal. We use this technical result to justify a calculation
in the physics literature describing algebras that are derived equivalent
to certain non-compact Calabi-Yau three-folds. Since the calculation produces
superpotentials for these algebras we also include some discussion
of superpotential algebras and their invariants.