Jax is a awesome champ, thats a fact, with those itens and masteries you will be able to kill any champion,but Jax is a hard champ to play, you must be able to coordinate your movements, chasing champs is one of jax best skills, he can chase with mastery, but like i said is hard,
because you need to get attacked to be able to dodge, and if you got the ''dodge'' you will be able to stun, but if your oponent is running he can't hit you, so? The answer lays on the minions, you must chase and receive the attacks of the minions to dodge, then you will be able to stun your oponent, and still run after him, If you notice that other champions are coming, you should return immediately, Jax passive gives him a LOT of life, so when you got infinity's edge you will have probably 3500 of life, and that scares a lot, a champ with enormous life and powerfull attack, but many people who plays with jax gets cocky at middle game, so you CAN'T get into 1x2 fights, cause you will probably lose,one more thing, you should not fight ranged enemies in a free fight, you must trap them and dominate the map, to appear at the right time and get the kill.

Like i said before, jax passive gives a lot of life, because you will receive life calculated by the ammount of attack damage and ability power that you have, with those itens you will be really strong, if you play right with jax probably, you will not be able to get Rabadon's Deathcap, because the game will end before you get the money to buy it.

Is a really important issue, Jax can farm really fast with counter strike and with RELENTLESS ASSAULT, any time in the game he can kill a lot of minions, but you should be carefull at early game, don't be greedy and don't hurry up to get the kills, cause if you don't you will feed your enemys, and nobody wants that.