For the function f(x) = xe^(3-(x/4)), which one of the following statements is true?

A. x = 4 is a critical number at which f has a local minimum.

B. x = 4 is a critical number at which f has a local maximum.

C. x = 4 is a critical number at which f has an inflection point.

D. x = 4 is not a critical number but f has an inflection point there.

E. x = 4 is a critical number but f does not have a local extremum nor an inflection point there.

F. x = 4 is not in the domain of f.