1define a function f(x) = x^(1/x)
f'(x) = x^(1/x) (1-lnx)x^2
=> f'(x) <0 when x > e
=> f(x) is a decreasing function for x>2.7
=> f(2011) > f(2012)
=> raising both sides to the power 2011.2012
=> 2011^(2012) > 2012^(2011)
\hspace{-16}$Which one is Greater $\mathbf{2011^{2012}}$ OR $\mathbf{2012^{2011}}$
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