The claim amount for an insurer is given by the function f(x) = 4x2e^(-2x) for x > 0 and 0 elsewhere.

i) Derive the moment generating function of x.
ii) Determine the variance of x.

Which of the following options correctly represents the moment generating function of x?

A) 4e^(2t)/(t-2)3
B) 4e^(2t)/(t+2)3
C) 4e^(-2t)/(t-2)3
D) 4e^(-2t)/(t+2)3