为什么∫ (x,0)f(t)dt≦xf(x)

Question

如题所述

Answer 1

令g（x）=积分（0,x）f(t)dt－xf(x)求导
g(x)‘=-xf(x)‘
因为f(x)在0到无穷单调递增所以f(x)≥0,g(x)‘≤0又g(0)=0所以g(x)在0到无穷≤0，得证