The number of points of local maxima of the function  $f\left(x\right)={(x-2)}^{2/3}(2x+1)$ is

$f\text{'}\left(x\right)={(x-2)}^{2/3}2+(2x+1)\frac{2}{3}{(x-2)}^{-1/3}=\frac{6(x-2)+2(2x+1)}{3{(x-2)}^{1/3}}=\frac{10x-10}{3{(x-2)}^{1/3}}$

$x=1$is a point of local maximum and $x=2$is a point of local minimum 

 $\therefore$ No.of extremum points is 2