Last Whisper becomes more effective at penetrating armor than The Brutalizer when an opponent has more than 28.6 armor. It becomes more effective than Youmuu's Ghostblade at 57.1 armor. It becomes more effective than five stacks of The Black Cleaver's debuff (plus its flat penetration) at 100 armor.
If the increased physical damage from the 35% amour penetration can be thought of as increased AD, the passive must increase damage by 23.89 points (860g/36g per AD = 23.89 AD), in order to be gold efficient.
For this to occur, “Arm*(AD-44.367) > 6825.7”, where Arm is the targets armour. This can be rounded to “Arm*(AD-45) > 7000”, for ease of remembering. A graph of the unrounded equation can be seen to the right.