This is the 1318th most frequent Polish word.
największej
"Największej" means "the biggest" or "the greatest" (feminine singular genitive form).
Here, 'największej' is used as a genitive form to describe a characteristic (greatness) belonging to the feminine noun 'radość' (joy).
To była największej radość mojego życia.
It was the greatest joy of my life.
Here, 'największej' is used adverbially to indicate an extent or degree describing how much something applies.
W największej mierze zależy to od twojego zaangażowania.
It depends on your commitment to the greatest degree.
In this sentence, 'największej' functions as a form modifying the feminine noun 'miłości' (love), showing the highest degree of a quality.