Power of the most powerful test for two densities on the unit interval

Let $X$ be a random variable of continuous type with probability density function $f(x)$. Then, based on single observation $X$, the most powerful test of size $\alpha=0.1$ for testing $H_0:f(x)=2x$, $0<x<1$, against $H_1:f(x)=4x^3$, $0<x<1$, has power