I have the following sentences.
The cars underwent fast changes from the application of mechanical technology to digital that currently take advantage of artificial intelligence.
The cars underwent fast changes from the application of mechanical technology to digital that currently taking advantage of artificial intelligence.
I am not sure, which sentence is correct?
Here the verb “to take” is being applied to the noun “technology”. In a much simpler form, the sentence would be
Technology takes advantage of (something)
This is still the correct form to use when additional qualifiers and elements of speech are included. Additionally though, I would point out that while many different components of many different cars have changed from mechanical to digital, you are really talking about a single change in the technology used to make cars. So I would say instead
The cars underwent a rapid change from the application of mechanical technology to digital, that currently takes advantage of artificial intelligence.
Edit: Another possibility, that makes one of your initial forms correct in this context, is to say
…that is currently taking advantage of…