13. [5] Find the number of real zeros of $x^{3}-x^{2}-x+2$.
Solution: Let $f(x)=x^{3}-x^{2}-x+2$, so $f^{\prime}(x)=3 x^{2}-2 x-1$. The slope is zero when $3 x^{2}-2 x-1=0$, where $x=-\frac{1}{3}$ and $x=1$. Now $f\left(\frac{1}{3}\right)>0$ and $f(1)>0$, so there are no zeros between $x=-\frac{1}{3}$ and $x=1$. Since $\lim _{x \rightarrow+\infty} f(x)>0$, there are no zeros for $x>1$. Since $\lim f(x)<0$, there is one zero for $x<-\frac{1}{3}$, for a total of 1 zero.