Increasing and decreasing intervals of a function

$f(x)={x}^{3}-4{x}^{2}+2$, which of the following statements are true:

(1) Increasing in $(-\mathrm{\infty},0)$, decreasing in $(\frac{8}{3},+\mathrm{\infty})$.

(2) Increasing in both $(-\mathrm{\infty},0)$, decreasing in $(\frac{8}{3},+\mathrm{\infty})$.

(3) decreasing in both $(-\mathrm{\infty},0)$, and $(\frac{8}{3},+\mathrm{\infty})$.

(4) Decreasing in $(-\mathrm{\infty},0)$, Increasing in $(\frac{8}{3},+\mathrm{\infty})$.

(5) None of the above.

${f}^{\prime}(x)=0=3{x}^{2}-8x=0\Rightarrow x=\frac{8}{3},x=0$ are the singular point/point of inflection.Could anyone tell me what next?

$f(x)={x}^{3}-4{x}^{2}+2$, which of the following statements are true:

(1) Increasing in $(-\mathrm{\infty},0)$, decreasing in $(\frac{8}{3},+\mathrm{\infty})$.

(2) Increasing in both $(-\mathrm{\infty},0)$, decreasing in $(\frac{8}{3},+\mathrm{\infty})$.

(3) decreasing in both $(-\mathrm{\infty},0)$, and $(\frac{8}{3},+\mathrm{\infty})$.

(4) Decreasing in $(-\mathrm{\infty},0)$, Increasing in $(\frac{8}{3},+\mathrm{\infty})$.

(5) None of the above.

${f}^{\prime}(x)=0=3{x}^{2}-8x=0\Rightarrow x=\frac{8}{3},x=0$ are the singular point/point of inflection.Could anyone tell me what next?