With respect to the original: y=x(1-x)^.4 - certainly appropriate for the undergrad via analytic methods. But if we generalize to: y^y=x(1-x)^x then can the original question still be answered (especially if the solution consists of 3 families of singularities)? Gary Tupper, Terrace B.C.

Related URL: http://www.peda.com

Why not consider the more general problem of f(x) = x^{p} (1-x)^{q} since I find the above example is too specific and the general problem is more interesting because f(x) is the integrand of the Beta integral. Just a suggestion, Sir Isaac