The doctors are busy doing what they can _____ the dying man.为什么是C.to save

to save the dying man是 what they can do 的目的状语

俺来解释吧
你把句子还原下就知道了
首先what=something that
the doctors are doing something ( what they can ) to save the dying man.

The doctors are busy doing (what they can) to save the dying man.
缩减为
The doctors (are busy doing to )save the (dying） man
be busy doing sth to ...忙着为什么而做什么
I am working hard to get high marks..

to save 动词不定式做目的状语

可以改写成：thedoctorsarebusydoingwhattheycandotosavethedyingman.它省略了do，

作目的状语，不定式的用法what 引导的是宾语从句

因为can 后面的do和前面的doing是一个动作,所以省略了
而to save the dying man是 what they can do 的目的状语
医生们忙着尽力去拯救那个快死的人

是解救的意思，解救正在死去的男人 。C是选项吧？