As the
conjunctive form of the
classical auxiliary verb べし,
べく will be attached to the
dictionary form of verbs in order to convey the purpose of an action. This will be translated as 'for the purpose of (A), (B)', 'in order to (A), (B)', or 'to ensure that (A), (B)'.
べく itself will only attach to verbs that can be done intentionally, with some purpose in mind. The (B) part of
べく sentences will also indicate an intentional action that will be performed in order to reach the goal of (A).
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地域（ちいき）の高齢者（こうれいしゃ）の安全（あんぜん）を守（まも）るべく、交番（こうばん）が設置（せっち）されました。
In order to ensure the safety of the elderly in the community, a police box has been set.
息子（むすこ）は医者（いしゃ）になるべく、ここ3年間（ねんかん）ほぼ寝（ね）ずに毎日（まいにち）勉強（べんきょう）をしている。
In order to become a doctor, he has been studying these past 3 years without much sleep.
When combining with する with
べく, due to
べく being a
classical auxiliary verb, it will attach to the classical stem of する, す. However, in modern Japanese it is fairly common to see both
すべく and
するべく, with both forms being considered correct.
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ここでの交通（こうつう）事故（じこ）を防止（ぼうし）すべく、ガードレールなどの設備（せつび）を設置（せっち）することになった。
In order to prevent car accidents here, things such as guardrails are to be installed.
次（つぎ）の大会（たいかい）で優勝（ゆうしょう）するべく、彼（かれ）らは毎日（まいにち）朝（あさ）から夜（よる）まで練習（れんしゅう）をするようにしている。
They try to practice every day from morning to night in order to win the next competition.
べく itself is a very formal structure in modern Japanese, so will rarely be used in standard speech.
Although べし and all of its conjugations have slightly different translations based on the grammar points that they appear in, the underlying meaning can be stemmed from the originating kanji 可（べ）し, meaning 'to be permissible'. The focus with this kanji and all forms of べし are just that the word it is attached to is being marked as a strong goal. This means that rather than 'in order to (A)', べく is closer to 'to attain (A)', in that it adds further emphasis.