Neyman-Pearson test at a named size

Consider the following two probability density functions (pdfs) $$f_{0}(x)=\begin{cases}2x,&\text{if }0\le x\le 1\\0,&\text{otherwise}\end{cases}\quad\text{and}\quad f_{1}(x)=\begin{cases}1,&\text{if }0\le x\le 1\\0,&\text{otherwise}\end{cases}$$ Let $X$ be a random variable having pdf $f\in\mathcal{F}=\{f_{0},f_{1}\}$. Consider testing $H_{0}:f(x)=f_{0}(x), \forall\,x\in[0,1]$ against $H_{1}:f(x)=f_{1}(x), \forall\,x\in[0,1]$ at $\alpha=0.05$ level of significance. For which of the following observed values of random observation $X$, the most powerful test would reject $H_{0}$?