f'(x)=3x²≥0,函數(shù)是增函數(shù).
用定義證也可以的：
設(shè)x1
=x2³-x1³
=(x2-x1)(x2²+x1x2+x1²)
=(x2-x1)[(x2+ x1/2)²+3x1²/4]
x2>x1x2-x1>0
平方項恒非負,(x2+x1/2)²≥0,3x1²/4≥0
3x1²/4=0時,x1=0 ,此時x2>0 (x2+x1/2)²=x2²>0,即兩不等式等號不同時取到.(x2+x1/2)²+3x1²/4>0
(x2-x1)[(x2+x1/2)²+3x1²/4]>0
f(x2)>f(x1)
函數(shù)是增函數(shù).