Optimizing the "Cool Function"

Algebra Level 4

Let the Cool Function ff be defined from the positive reals by f(x,y,z,t)=(x2+2x+1)(y2+2y+1)(z2+z+1)(t2+t+1)xyztf(x,y,z,t) = \frac{(x^{2} + 2x + 1)(y^{2} + 2y + 1)(z^{2} + z + 1)(t^{2} + t + 1)}{xyzt} Find the minimum value of ff.

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