"Do the utmost" is correct and usable in written English.
You can use it when you want to express the idea of doing something with great effort, skill, or dedication. For example, "I'm determined to do the utmost to ensure my team's success this season."
"And let's do the utmost to make the American people proud of our efforts".
Kan later said that he intended "to do the utmost as finance minister".
It can also cover failing "to do the utmost to capture or destroy enemy troops".
"We have to do the utmost to live up to the expectations," Mr. Hassan said, "and don't forget the expectations are very high here in the region.
But sport is a very important social activity, and we have to do the utmost to preserve and protect the activity of the International Skating Union".
Americans expect their government to do the utmost to protect our country, but that cannot mean trading our Fourth Amendment right to privacy for the promise of security.
They resumed the old Medicean practice of trading on their own account, and, without reaping much benefit thereby, did the utmost damage to private enterprise.
However, J Edgar Hoover and the FBI did the utmost to "neutralise" and undermine the party by recruiting informers and spreading misinformation about the organisation.
In a statement, WhatsApp said the company was "disappointed at the decision" after doing the utmost to cooperate with Brazilian tribunals.
"So we have many reasons, both moral and political, for doing the utmost to make sure that our strikes are as surgical as possible".
They are about doing the utmost to extract the last drops from a finite life, if not for their own sake then for the sake of a child's graduation, a grandchild's birth, a friend's wedding.
