Which is bigger: or ?
We know that .
Let us conjecture that .
This means that , that is, . Therefore, if our conjecture is true, we must have .
Let us consider the function . Find its minimum on . You will find that the minimum of is , and this minimum is reached when .
But we know that , thus the minimum is never reached with .
. You can follow the steps backwards to finally prove that
That was the nearly-complete proof. Now, you only have to show that the minimum of is when , and you are done
Lol, I wasn't sure my proof was going to pass since this is the algebra forum and my proof is already half-way into calculus, but Drex actually brought in the integral !
Nice proof though, everything is already trivially proved and one just has to put the bits together