It is difficult to differentiate these two words. I think it helps a bit to say "fast" refers to movement, "quick" to reaction. But a lot of uses are idiomatic and a matter of the dictionary. A clean differentiation of "fast" and "quick" is not possible as there is an overlapping area. The matter is complicated as "fast" has two meanings, it can refer to speed and it can express firmness. Dictionaries should have two entries, but often "fast 1" and "fast 2" are intermingled in one dictionary entry. Normally dictionaries are not very good at differentiating words whose meanings are very close. If you compare dictionary explanations of "fast" and "quick" you often find such definitions/explanations don't help at all. Often dictionaries with up-to-date lexicology try to solve such problems by giving a special information box where more information about the use of words with similar meanings is given. But I haven't seen such an information box for "fast" and "quick" yet.
