Fast is an adjective that means swift or able to move rapidly. It is usually used in reference to speed.
Example: The PDC bit was fast in that formation, whereas the tricone drill bit was slow.
Quickly is an adverb that means promptly or taking very little time to happen.
Example: With the PDC bit we were able to drill the well quickly, whereas the tricone bit drilled more slowly.
Adjectives use the suffixes –er and –est to make the comparative and superlative forms, respectively.
Faster – comparative
Slowest – superlative
Adverbs use “more” and “most” before them to make the comparative and superlative forms, respectively.
More quickly – comparative
Most slowly – superlative
However, there are some instances when “fast” can be used as an adverb rather than an adjective.
Merriam-Webster dictionary has noted some common “flat” adverbs that have dropped the –ly commonly found at the end, making them sound more like an adjective, but are still used to modify a verb (something only an adverb can do.)
Drive slow – drive slowly means the same thing.
Eat fast – means the same as eat quickly, but sounds much faster.
Shine bright – means the same as shine brightly.
Go quick – means the same as go quickly.
Work hard – does NOT mean the same as hardly working!
Here are some other examples of “flat” adverbs:
Sounds like good advice to me!