Most often describes something with a sharp cutting edge or point, such as a knife, blade, or instrument. It is more formal and descriptive than everyday 鋭い.
The perpetrator is believed to have used a sharp blade.
I cut my finger with a sharp blade.
この作業には鋭利な工具を使う。
This task uses sharp tools.
Figurative use for a keen mind, incisive analysis, or acute perception; it tends to sound written or formal, and 鋭い is the more common everyday choice.
彼女の批評は鋭利で、無駄がない。
Her criticism is incisive and has no wasted words.
The wound showed a clean, sharp-cut edge.
With her sharp mind, she solved one difficult problem after another.
This reporter depicts the hidden side of society with keen observational insight.
鋭敏 emphasizes keenness of the senses or intuition (e.g. a sharp sense of smell), while 鋭利 focuses more on cutting sharpness or incisive reasoning.
尖鋭 describes something sharply pointed or, figuratively, radical/extreme in stance, whereas 鋭利 stresses cutting keenness or mental incisiveness without the radical nuance.
切れ味 describes how well a blade actually cuts, while 鋭利 describes general sharpness or keenness, whether of an edge or a mind.
鈍い means dull or blunt, the direct opposite of 鋭利 whether describing a blade's edge or a person's mental sharpness.
鋭意 shares the kanji 鋭 with 鋭利 but means 'earnestly, diligently' (as in 鋭意努力する), not sharpness at all.
鋭利 describes physical sharpness of a blade or edge, while 鋭敏 describes sharpness of senses or intellect, not physical cutting ability.
Standard kanji spelling; mainly used in somewhat formal descriptions of sharp blades, tools, points, or keen perception.
A Sino-Japanese compound written with 鋭, associated with sharpness or keenness, and 利, associated here with sharpness or effectiveness. This is a component-based explanation of the written form, not a claim about the full historical derivation.