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Mar 19, 2013 at 16:20 comment added Dima Pasechnik it might not come to quantifier elimination. Generically, $f'(x)=0$ together with the equations for extra variables needed for getting rid of square roots and the denominator will give you a 0-dimensional ideal. Then you're almost done...
Mar 19, 2013 at 12:09 comment added H A Helfgott I had thought of this. But don't quantifier-elimination programs have a horrid dependence on the number of variables? In my experience, QEPCAD does fine on 1 or 2 variables, but chokes on 3.
Mar 19, 2013 at 1:30 history answered Dima Pasechnik CC BY-SA 3.0