尽(jìn) - to exhaust, to use up; to the utmost, to the full; the end, the limit in Mandarin

尽 means finished to the last drop. As a verb it is to exhaust or to discharge fully: 尽力 (do one's utmost), 尽责 (do one's duty), 尽我所能 (all I can). As a resultative ending on another verb it means the action ran the thing dry: 用尽 (used up), 吃尽苦头 (went through every hardship).

The noun sense is the limit or end point, which gives 尽头 (the far end of a road or corridor) and 无尽 (endless). Same idea, different grammatical hat.

The trap is that this character has a second reading, jǐn, with a rather different job: 尽快 (as soon as possible), 尽量 (as far as possible), 尽管 (although, go right ahead). Those are all third tone, not fourth. If the word means "as much as you can" you are probably looking at jǐn; if it means "used up" or "to the utmost", it is jìn.