NIMCET 2024 — Mathematics PYQ

$f(x)=x^{2/3}\cdot (6-x{)}^{1/3}$  
$f^{\prime }(x)=x^{2/3}\cdot \frac{1}{3}\cdot (6-x{)}^{-2/3}+\frac{2}{3}\cdot (6-x{)}^{1/3}\cdot x^{-1/3}$  
$f^{\prime }(x)=x^{-1/3}\cdot (6-x{)}^{-2/3}\cdot \left(-\frac{x}{3}+\frac{2}{3}(6-x)\right)$  
$f^{\prime }(x)=\frac{1}{x^{1/3}(x-6{)}^{2/3}}\left(-\frac{x}{3}+4-\frac{2x}{3}\right)$  
$f^{\prime }(x)=-\frac{1}{x^{1/3}(x-6{)}^{2/3}}(x-4)$  
$f$ has a point of inflection at $x=0$