Abstract: Okamoto's one-parameter family of self-affine functions includes functions of Perkins and Bourbaki/Katsuura, as well as the classical Cantor function. In this talk I will give an exact characterization of the set D of points where these functions have an infinite derivative. This set turns out to be very closely related to the set of real numbers having a unique beta-expansion. As a result, the so-called Komornik-Loreti constant (which is intimately related to the Thue-Morse sequence) separates parameter values for which D is countable from those for which D has strictly positive Hausdorff dimension. If time permits, I will also discuss the Hausdorff dimension of the set of (non)differentiability points of Okamoto's functions.​