用定义证明f(x)=x^3的单调性

网友回答

x1,x2∈(-∞,+∞) x1>x2f(x1)-f(x2)
=x1^3-x2^3
=(x1-x2)(x1^2+x1x2+x2^2)
=(x1-x2)[(x1+x2/2)^2+(3/4)*x2^2]
[x1>x2 x1-x2>0(x1+x2/2)^2+(3/4)*x2^2>0]>0可知f(x)在R上单调递增