Some of those are continuous and differentiable everywhere. Examples: f(x) = 0 f(x) = ½ x² Also: doesn’t the claim that you can pick such a function requi

Some of those are continuous and differentiable everywhere. Examples: f(x) = 0 f(x) = ½ x² Also: doesn’t the claim that you can pick such a function require an extreme version of the axiom of choice, where you claim you can pick an element of each set in a set of sets that has uncountably many items?