The Lambert function, the quintic equation and the proactive discovery of the Implicit Function Theorem

One of the problems on which a great deal of focus is being placed today, is how to teach Calculus in the presence of the massive diffusion of Computer Algebra tools and online resources among students. The essence of the problem lies in the fact that, during the problem solving activities, almost all undergraduates can be exposed to certain ''new'' functions, not typically treated at their level. This, without being prepared to handle them or,...