So Sated Devourer just came out.
As you know, it's extremely powerful on Jax.
Here is why:
1. The passive gets to maximum stacks in 4 autos instead of 6.
2. After 3 auto-attacks his R-Passive (Additional Magic Damage) procs every other auto-attack instead of every 3.

This may have just brought back AP Jax.

Max Attack speed explanation:
So, according to the page below, Jax reaches the Maximum amount of attack speed (2.5)
when you add an extra 234.2% attack speed.
http://leagueoflegends.wikia.com/wiki/List_of_champions%27_attack_speed

With my build you get an extra 234.1%

Calculations:
50% from Devourer
+50% from Wit's End= 100%
+40% from Botrk= 140%
+84% from Jax Passive= 224%
+5% from Masteries= 229%
+5.1% from Runes= 234.1%

The best part is that Sated Devourer gets you to 6 stacks of passive
after 4 auto-attacks instead of 6.

Max Cooldown explanation:
5% from Masteries
5% from Runes:
10% from Spirit Visage
20% from Frozen Heart

I chose 3 Attack Speed Marks because that's all I needed
to hit the maximum of 234.2% Attack Speed which this build is based off of.

I chose Two 3% Lifesteal Quints because with Sated devourer you need to be able to
stay in the jungle as long as you can getting those Devourer Stacks, and this also
allows you to get Stalkers Blade instead of Rangers, you really need the Stalkers
Blade to keep up while ganking.

I chose 6 Cooldown Glyphs to Reach 5% which was needed to hit the 40% CDR Maximum.

I chose 3 Armor Glyphs to take less damage in the jungle.

I chose 9 Armor Seals to take less damage in the jungle.

I chose 6 Attack Damage Marks since I didn't need any more attack speed, you can
also switch these with armor penetration if you want.

I chose 1 Attack Damage Quint because I didn't need any more attack speed, you
can also switch this out for armor penetration or move speed or another 1.5%
Lifesteal if you so choose.

Devourer:
The 50% Attack speed helps reach the Attack Speed Cap.
The 60 Magic Damage on hit at 30 stacks deals a ton of magic damage every auto,
which gets boosted by having maximum attack speed.
Sated Devourer is an obvious choice for Jax. When Sated, his R passive procs every other auto-attack instad of every 3 auto-attacks. (So OP)
When Sated, you only need 4 auto-attacks to reach maximum passive stacks of 6,
instead of 6 auto-attacks before Sated.
This build is based off of the R Passive, so that's why I went for the limit
of 2.5 Attack Speed. The more R Passive Procs, the more OP.
Important Note: You gain stacks from takedowns and not last hits.
For example, your mid-laner wants blue buff. As long as you are there attacking
Blue and you attacked blue a couple seconds before he finished it off, you
will get a Devourer stack and he will get Blue buff.

Stalkers Blade Smite instead of others:
Extremely helpful for ganking lanes, allows you to slow them down before they can
run to their turret. Also helps you get away when being chased. Also helps finish
off an enemy who is one hit from death but getting away while your Q is on cooldown.

Boots of Mobility with Homeguards:
Since this build is based around hitting 30 stacks ASAP. You need to be able to
run from camp to camp as fast as possible so you can farm and stack as fast as possible.
This also helps with running to gank a lane extremely fast and running to Dragon in time.
You need homeguards early so you can get back to farming faster. Get to dragon incredibly fast. Help a teammate who is getting chase. Run to Gank a lane incredibly fast.

Blade of the Ruined King:
The 40% Attack speed helps reach the Attack Speed limit for the build.
The Active is insanely helpful for either ganking or getting away when being chased,
it can even be used to finish off an enemy who could have gotten away.
The 25 AD helps with damage.
The 10% Lifesteal is a must for staying alive in 1v1's and teamfights and killing
Baron Dragon. Combine this with Sated Devourer and every other auto-attack makes it 20% lifesteal. Which is boosted by having 2.5 Attack Speed.
The Passive is insane because it deals an EXTRA 8% of the targets
current HP on hit. Combine this with Sated Devourer and the passive procs twice
every other auto-attack! Which is boosted by having 2.5 Attack speed.

Wit's End:
The 50% attack speed helps reach the Attack speed Cap.
One Passive adds 42 Bonus Magic damage on hit, which is very strong combined with having maximum attack speed!
The Other passive steals 5 MR every hit up to 25 MR. Which gives you 25 MR which makes you tankier against AP damage. And it makes your target more prone to your AP damage since they have 25 less MR.
The 30 MR on top of that helps against AP damage.

Frozen Heart:
The 100 Armor helps a lot against AD damage dealers.
The 400 Mana helps you not run out.
The 20% Cooldown Reduction is Vital! Since Jax abilities are so important.
The Aura which reduces the attack speed of nearby enemies by 15% helps you a ton
against a fast auto-attacker in a 1v1. And also helps a ton while in a teamfight
because it reduces all enemy champion attack speeds by 15%.

Spirit Visage:
400 Health helps a ton for staying alive.
55 Magic Resist is vital for not getting one shot by mages.
100% Base HP Regen helps a ton for regaining health in-between fights and in fights.
10% Cooldown Reduction is vital to help get to 40% CDR.
The Passive which just got buffed is incredibly strong.
It increases all healing done to you by 20%
This includes healing from friendly champions like for example Soraka/Sona/Taric/Alistar.
This also includes Life steal, Spell Vamp, Health regeneration, Summoner Spell Heal.
Literally everything that regains your health gets boosted by 20%. OP.

Situational Items:

Hextech Gunblade:
You can get this if you are way ahead in the game.
40 AD helps damage of course.
80 AP helps deal extra damage with your W proc and R passive proc.
10% Lifesteal adds to the 10% from Botrk and heals you for a ton!
20% Spell Vamp heals you for a TON because of how much AP spell damage you deal.
The active is just like Blade of the ruined king active but it slows them by
40% instead of 25%. Combine both actives with stalkers blade smite and you can keep
an enemy champion slowed down for a while!
The passive reduces the cooldown of the active, and since this build is based off
having maximum attack speed. you can get your active back incredibly quick.

Will of the Ancients:
You can get this if you are way ahead and have Hextech already.
The 80 AP helps a ton for W proc and R passive proc damage.
The 10% cooldown reduction helps.
The passive heals you for 15% of the damage dealt by your spells and abilities,
before your targets resistances! So this includes Q, W proc, E damage, and R passive proc.
Pretty much all sources of your damage except auto attacks!
This will heal you for tons!

Because of the 3% Lifesteal Quints, you can go a lot further,
and it isn't required to get Ranger's Trailblazer.

Jungle Route:
Start Whichever side your adc is on.
Ask for a good leash.

Example from Blue Side:
Start Krugs (Rock guys) At 1:45, place a ward in the bush next to red buff.
Proceed onto Red buff. Pop a potion.
Then raptors.
Then wolves. Pop a potion.
Then blue buff.
Then Gromp.
Then Scuttles.
Gank if there is a good opportunity.
If not, head to raptors.
Then to Krugs.
Then Recall.
Grab Warriors Blade and 2 Daggers.
Head to Wolves.
Then Gromp.
Then Raptors and Krugs and Red buff.
Should be enough for Devourer and Lvl 6.
Recall grab Devourers and head to Dragon (you can solo now)

Start JG item and 2 HP Pots.
Devourer.
Boots of mobility. (Homeguards if enough)
Blade of the Ruined King.

Now this is where you can choose next item based on game.
If you are falling behind,
Build either Frozen Heart or Spirit Visage depending
on if their AD or AP champs are more fed.

If you are ahead grab wit's end before the Frozen Heart and Spirit Visage.

If you are REALLY ahead. Get a Hextech Gunblade after wit's end.
With only these 5 items you can solo baron and come out with almost full HP.
I've done this at 25 minutes before.

If you're ballsy after Hextech Gunblade you can grab
Will of the Ancient's. These will equal to 160 AP which
helps a ton for Jax W and R Passive. This will also equal to 20% Spell Vamp.
Which works with W passive and R passive. Will of the ancients will
also heal you for 15% of all damage dealt BEFORE Resistances, with spells and abilties, which also works with W passive and R passive.
This leads to INSANE healing, but the downside is getting cc'd and bursted.

If you reach maximum build, you can swap Boots of mobility for
Mercury Treads.

Then you can grab an Elixir. I recommend Elixir of Iron,
Because with that and Mercury Treads and Tenacious Mastery. You're at 70% Tenacity.