f(x)=x^3-4
设x1、x2∈R,x1>x2,
则f(x1)=x1³-4,f(x2)=x2³-4,
=> f(x1)-f(x2)=x1³-x2³=(x1-x2)(x1²+x1x2+x2²)=(x1-x2)[(x1+x2/2)²+3x2²/4]
x1>x2,=>x1-x2>0;
x1²+x1x2+x2²=[(x1+x2/2)²+3x2²/4]>0恒成立;
=> f(x1)-f(x2)>0
=> f(x1)>f(x2)
=> 函数f(x)=x^3-4在R上为单调递增函数