How do I show that for all $x,y\geq 0$, $\frac{x^2+y^2}{4}\leq e^{x+y-2}$? Tried using the mean value theorem but couldn't figure out how to use it properly.


marked as duplicate by Claude Leibovici, vrugtehagel, Mark, pre-kidney, JonMark Perry Mar 26 '17 at 8:19

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  • $\begingroup$ Expand the series of e^(x+y+2) and see that there are positive terms other than x^2+y^2/4 $\endgroup$ – user8795 Mar 26 '17 at 7:50
  • $\begingroup$ @user8795 the question is asking for $e^{x+y-2}$, so the series would contain positive and negative terms, so that method does not work directly. $\endgroup$ – adfriedman Mar 26 '17 at 7:53