Finding values for x at which a function is differentiable

Question

Without graphing, how would you be able to find where a function is differentiable and the points where it is not?

Answer 1

The answer to this question depends on the function and whether you are discussing real valued functions or complex valued functions...or even functions defined in some other way. The more experience you have with functions, the more likely you are to find troublesome points. And even then you may be surprised at the behavior of functions which initially seem to be "nice".