Finding the MLE of $\theta$ where $\theta \leq x$ consider the following PDF
$$
\begin{eqnarray}
f(x;\theta) &=&
\left\{\begin{array}{ll}
2\frac{\theta^2}{x^3} & \theta \leqslant x\\
0 & x< \theta; 0 < \theta
\end{array}\right.\\
\end{eqnarray}
$$
Now the answer stats $X_{1:n}$ so the minimum of $X$, but this cannot be deduced from the answer via my normal method (log likelihood), how am I to approach this, and other questions like it? 

Hint: At what value of $\theta$ is the likelihood maximized keeping in mind that $\theta \le x_i$ for all $i$?
