(x, y) = (| relative maxima relative minima (х, у) %3D points of inflection (х, у) %- (smaller x-value) points of inflection (х, у) - (larger x-value)

The given function is $y=x^{1/3}(x-8)$.

The first and the second derivative of y is $y\text{'}=\frac{4(x-2)}{3x^{{\displaystyle \frac{2}{3}}}} ...... \left(1\right).$

The second derivative of y is $y\text{'}\text{'}=\frac{4(x+4)}{9x^{{\displaystyle \frac{5}{3}}}} ...... \left(2\right).$

Compute the relative extrema as follows.

Substitute y'=0 in equation (1).

$$\begin{gathered} \frac{4(x-2)}{3x^{{\displaystyle \frac{2}{3}}}}=0 \\ 4(x-2)=0 \\ x=2 \end{gathered}$$

The $y\text{'}=\frac{4(x-2)}{3x^{{\displaystyle \frac{2}{3}}}}$is observed to be undefined at x=0.

Thus, the critical points are x=0 and x=2.