Advanced Statistics Questions

I have two questions:

1) Let X_1, X_2, ..., X_n be i.i.d. from a distribution with pdf:

http://img412.imageshack.us/img412/8497/3a1s.gif

I am supposed to find the MLE (maxmium likelihood estimator) for theda. However, if I take the derivative of the likelihood function (Likelihood function given below) and set it equal to zero, it doesn't work.

http://img527.imageshack.us/img527/9905/3a2.gif

I must maximize the likelihood function a different way then. I argue that in order for the likelihood function to be maximized,

http://img402.imageshack.us/img402/7738/3a3.gif (which is the first order statistic; thus "theda hat" equals the minimum).

**Is my logic correct?**

2) Let X_1, X_2, ..., X_n be i.i.d. with distribution Laplace(u,1). Find the Fisher information for u.

Here's the pdf:

http://img151.imageshack.us/img151/7446/4a1.gif

When I solve the Fisher information, I_n (u), I get zero... **is this right? If not, what is another way to solve it?**

Thanks for the help!