Durst is a verb.
According to Merriam Webster dictionary durst means: Archaic and dialect past of dare.
In other words, durst is an old fashion way of saying dare. It is also a way certain groups of people spoke depending on the social group they belonged to.
The word durst is used by Nathaniel Hawthorne on page six of the class handout entitled, “Young Goodman Brown.”
Nathaniel Hawthorne wrote, “Goodman Brown alternately crouched and stood on tip-toe, pulling aside the branches, and thrusting forth his head as far as he durst, without discerning a shadow.”
Goodman Brown was making his best effort to avoid being detected in the bushes by anyone passing. At the same time he wanted to see who was passing. He extended his head from the bushes as far as he thought would be appropriate for him to identify who is passing without them in turn seeing him.