For what values of $x$ is the rate of increase of $x^{3}-2x^{2}+3x+8$ is twice the rate of increase of $x$

Question

\[\begin{array}{1 1}(1)\bigg(-\frac{1}{3},-3\bigg)&(2)\bigg(\frac{1}{3},3\bigg)\\(3)\bigg(-\frac{1}{3},3\bigg)&(4)\bigg(\frac{1}{3},1\bigg)\end{array}\]