>>11423600With the Weierstrass substitution and dividing out the common polynomial factor , the expression becomes (thanks to computer algebra)
It is readily verified by standard analysis that the numerator has a single positive minimum, so the infimum is non-zero as the function tends to -2 at infinity.
It follows that the infimum is the absolute value of some local extrema of the rational function.
This rational function has a derivative whose real zeroes are
Substituting in, we find that the latter two points give the same, smallest absolute value of the function as .
