(1)构造指数函数f(t)=e^t,则f'(t)=e^t>0,f''(t)=e^t>0.故f(t)为下凸函数,依Jensen不等式得[f(x)+f(y)]/2>f[(x+y)/2](x≠y时为严格不等式)∴(e^x+e^y)/2>e^[(x+y)/2].(2)构造函数f(t)=tlnt (t>0),则f'(t)=lnt+1,f''(t...