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.

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