he/she addressed that - the points at which the function isn't differentiable has measure zero. besides this isn't some kind of new hack - one sided limits (and

he/she addressed that - the points at which the function isn't differentiable has measure zero. besides this isn't some kind of new hack - one sided limits (and therefore derivatives) were invented exactly for such cases (min, max, abs) and have been used by mathematicians probably since just about when calculus was invented.