Question

函数单调性的习题解答设f(x)在(0,+∞)上有定义,且 f(x)/x 在(0,+∞)内单调减小,证明：对任意两点x1>

Answer 1

设x1>0 ,x2>0且x1≤x2.

则f(x1+x2)/(x1+x2)≤f(x2)/x2,f(x2)/x2≤f(x1)/x1.

f(x1+x2)≤f(x2)+f(x2) x1/x2,f(x2) x1/x2≤f(x1).

所以f(x1+x2)≤f(x2)+f(x1).