Show that $f(x)=x^{3}$ is strictly increasing. (Hint: Consider the sign of $\left.x_{2}^{3}-x_{1}^{3}=\left(x_{2}- X_{1} ight)\left(x_{1}^{2}+x_{1} X_{2}+x_{2}^{2} ight)=\left(x_{2}- x_{1} ight)\left|\left(x_{1}+\frac{1}{2} x_{2} ight)^{2}+\frac{3}{4} x_{2}^{2} ight] . ight) S.P.PB. 357