Briefly explain what it means for a function to be differentiable at a point. Solution We say that function f is differentiable at the point a in its domain if f\'(a) exists. Differentiable on a Subset of the Domain The function f is differentiable on the subset S of its domain if it differentiable at each point of S. Note A function can fail to be differentiable at a point a if either lim h0 f(a+h) - f(a) h does not exist, or is infinite. In the former case, we sometimes have a cusp on the graph, and in the latter case, we get a point of vertical tangency. It means that the derivative exists at that point..