"he tried his utmost"

"extreme cold"
"extreme caution"
"extreme pleasure"
"utmost contempt"
"to the utmost degree"
"in the uttermost distress"

"to the last measure of human endurance"
"whether they were accomplices in the last degree or a lesser one was...to be determined individually"

"had traveled to the farthest frontier"
"don't go beyond the farthermost (or furthermost) tree"
"explored the furthest reaches of space"
"the utmost tip of the peninsula"