In which situation would a writer most likely use formal language? apex?

In situations which demand a quality written piece of work with no slang and complex prose, such as in articles or formal speeches, the writer should use formal language.

Explanation:

Formal use of language is necessary when a writer is confronted with an assignment or a client that demand complex prose and use of formal language throughout. In some situations a writer might need to write an article to be published in a top journal, or write a formal speech which will be read to in front of top executives, in which case he should use formal language

the communist manifesto is an 1848 political pamphlet by the german near the end of the manifesto, the authors call for a "forcible overthrow of all existing social conditions",  ..