Mathematics - Application of Derivative Question with Solution | TestHub

$$\begin{array}{l}\text{ Here, }\mathrm{f}(\mathrm{x})=(\mathrm{x}(\mathrm{x}-2){)}^2\\ \Rightarrow {\mathrm{f}}^{\prime }(\mathrm{x})=4\mathrm{x}(\mathrm{x}-2)(\mathrm{x}-1)\end{array}$$ For $\mathrm{f}(\mathrm{x})$ as increasing, ${\mathrm{f}}^{\prime }(\mathrm{x})>0$ $$\text{ So, }4x(x-1)(x-2)>0\Rightarrow x(x-1)(x-2)>0$$
From the above figure required interval is, (0,1)$\cup (2,\infty )$