Find an upper bound for the minimum of the functional

$\displaystyle J\{y\} = \int\begin{array}{cc}1\\0\end{array} y^2 y'^2 dx $

subject to y(0)=0 and y(1)=1 using te trial functions

$\displaystyle y_\epsilon(x)=x^\epsilon $ with $\displaystyle \epsilon > 1/4. $ Justify your argument.

Thanks in advance