Beta$(3,1)$ against uniform: the likelihood ratio $3x^2$ increases in $x$

Let X be a r.v. with first kind beta distribution with parameters $(\alpha,\beta)$. Then based on a single observation on X, Most Powerful test for testing $H_0:(\alpha,\beta)=(1,1)$ against $H_1:(\alpha,\beta)=(3,1)$ has critical region of the form: