Mathematics - Application of Derivative Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{f}(\mathrm{x})=(\mathrm{x}-2{)}^{2/3}(2\mathrm{x}+1)\\ & {\mathrm{f}}^{\prime }(\mathrm{x})=\frac{2}{3}(\mathrm{x}-2{)}^{-1/3}(2\mathrm{x}+1)+(\mathrm{x}-2{)}^{2/3}\\ & {\mathrm{f}}^{\prime }(\mathrm{x})=2\times \frac{(2\mathrm{x}+1)+(\mathrm{x}-2)}{3(\mathrm{x}-2{)}^{1/3}}\\ & \frac{3\mathrm{x}-1}{(\mathrm{x}-2{)}^{1/3}}=0\end{array}$ Critical points $\mathrm{x}=\frac{1}{3}$ and $\mathrm{x}=2$