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 $i$?