Whatever and whichever are two revved-up relative adjectives that you can use to jumpstart a dependent clause. But how do you know which one to use? Gentlemen and ladies, start your adjective engines:
Use whichever when the subject of the dependent clause is one of two or more known options. If you don't know all of the options available, use whatever.
Example
Jay will suck up to whatever of his twin brothers is most likely to loan him their car on Saturday night.
OR
Sandra's dad will pay for whatever repairs are needed to her Volkswagen.
We've really shifted these examples into top gear, haven't we? Can you tell which one uses whatever correctly?
It's the second one because the entire range of repair options after Sandra ruined her ride is unknown. Therefore, whatever is the way to go. In the first sentence, you should use whichever because Jay has clear set of options to choose from: one of two twins.