The function f(x)=(x(x-2))^ 2 is increasing in the set

$$\begin{array}{l}\text{ Here, } \mathrm{f}(\mathrm{x})=(\mathrm{x}(\mathrm{x}-2))^{2} \\ \Rightarrow \mathrmf^{\prime}(\mathrm{x})=4 \mathrm{x}(\mathrm{x}-2)(\mathrm{x}-1) \end{array}$$ For \mathrm{f}(\mathrm{x})$as increasing,$\mathrmf^{\prime}(\mathrm{x}) > 0\text{ So, }4 x(x-1)(x-2)>0 \Rightarrow x(x-1)(x-2)>0 $<img src="/api/proxy-image?url=https$ \\ From the above figure required interval is, (0,1)$\cup(2, \infty)