Young's Inequality can be restated as: s^(x)t^(1-x)<=xs + (1-x)t where s,t>=0 and 0<x<1. Basically i've been asked to prove this. I've been fiddling about with it for a couple of hours to no avail. I've tried to substitute t=e^u and s=e^v and then use partial differentiation w.r.t to v on st, but i'm not getting the required form. (I can't assume that exp is a convex function - otherwise it follows trivially) Thanks in advance.